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Theorem which asserts the existence of an object
In mathematics, an existence theorem is a theorem which asserts the existence of a certain object. It might be a statement which begins with the phrase
Existence_theorem
Theorem regarding the existence of a solution to a differential equation
Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees
Peano_existence_theorem
Existence and uniqueness of solutions to initial value problems
also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard
Picard–Lindelöf_theorem
Statement on solutions to ordinary differential equations
Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows
Carathéodory's existence theorem
Carathéodory's_existence_theorem
Theorem in complex analysis
In mathematics, specifically complex analysis, Riemann's existence theorem states that the category of compact Riemann surfaces is equivalent to the category
Riemann's_existence_theorem
System of mathematical set theory
finitely axiomatizable, while ZFC and MK are not. A key theorem of NBG is the class existence theorem, which states that for every formula whose quantifiers
Von Neumann–Bernays–Gödel set theory
Von_Neumann–Bernays–Gödel_set_theory
Fundamental theorem in mathematical logic
thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). Henkin's proof was simplified by Gisbert Hasenjaeger
Gödel's_completeness_theorem
Existence and uniqueness theorem for certain partial differential equations
the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential
Cauchy–Kovalevskaya_theorem
Consistent set of finite-dimensional distributions will define a stochastic process
extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees
Kolmogorov_extension_theorem
Index of articles associated with the same name
Black hole uniqueness theorem Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated
Uniqueness_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Property of artificial neural networks
but increasing its number of layers, making it "deeper." These are existence theorems. They guarantee that a network with the right structure exists, but
Universal approximation theorem
Universal_approximation_theorem
In mathematics, the Grothendieck existence theorem, introduced by Grothendieck (1961, section 5), gives conditions that enable one to lift infinitesimal
Grothendieck existence theorem
Grothendieck_existence_theorem
Method of proof in mathematics
non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing
Constructive_proof
Correspondence between finite abelian extensions and generalized ideal class groups
In class field theory, the Takagi existence theorem states that for any number field K there is a one-to-one inclusion reversing correspondence between
Takagi_existence_theorem
Every Riemannian manifold can be isometrically embedded into some Euclidean space
The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash Jr., state that every Riemannian manifold can be isometrically embedded
Nash_embedding_theorems
Mathematical concept
\end{aligned}}} There is a dual existence theorem for colimits in terms of coequalizers and coproducts. Both of these theorems give sufficient and necessary
Limit_(category_theory)
Two closely related mathematical subjects
an (smooth projective) algebraic curve. Under the name Riemann's existence theorem a deeper result on ramified coverings of a compact Riemann surface
Algebraic geometry and analytic geometry
Algebraic_geometry_and_analytic_geometry
On when a family of real, continuous functions has a uniformly convergent subsequence
family of functions. The theorem is the basis of many proofs in mathematics, including that of the Peano existence theorem in the theory of ordinary
Arzelà–Ascoli_theorem
Type of calculus problem
(1955, Theorem 1.3) or Robinson (2001, Theorem 2.6). An even more general result is the Carathéodory existence theorem, which proves existence for some
Initial_value_problem
State of being real
mathematical object matching a certain description exists is called an existence theorem. Metaphysicians of mathematics investigate whether mathematical objects
Existence
Theorem about metric spaces
Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important
Banach_fixed-point_theorem
Mathematics of real numbers and real functions
criteria of the Picard existence theorem do not hold. An example application is the Peano existence theorem. The Arzelà–Ascoli theorem is itself a kind of
Real_analysis
Result in combinatorics and graph theory
mathematics, Hall's marriage theorem, proved by Philip Hall (1935), is a theorem with two equivalent formulations. In each case, the theorem gives a necessary and
Hall's_marriage_theorem
One of two theorems in dynamical systems
Krylov–Bogolyubov theorem (also known as the existence of invariant measures theorem) may refer to either of the two related fundamental theorems within the
Krylov–Bogolyubov_theorem
Type of functional equation (mathematics)
subjects of interest. For a first-order initial value problem, the Peano existence theorem gives one set of circumstances in which a solution exists. Given any
Differential_equation
Topics referred to by the same term
theorem (convex hull), about the convex hulls of sets in R d {\displaystyle \mathbb {R} ^{d}} Carathéodory's existence theorem, about the existence of
Carathéodory's_theorem
Well-quasi-ordering of finite trees
under homeomorphic embedding. A finitary application of the theorem gives the existence of a fast-growing TREE function. TREE(3) is one of the largest
Kruskal's_tree_theorem
cohomology Hasse norm theorem Herbrand quotient Hilbert class field Kronecker–Weber theorem Local class field theory Takagi existence theorem Tate cohomology
Class_formation
Differential equation that is linear with respect to the unknown function
case of an ordinary differential operator of order n, Carathéodory's existence theorem implies that, under very mild conditions, the kernel of L is a vector
Linear_differential_equation
On the remainder of division by x – r
polynomial remainder theorem and the existence part of the theorem of Euclidean division for this specific case. The polynomial remainder theorem may be used to
Polynomial_remainder_theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Existence and cardinality of models of logical theories
In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf
Löwenheim–Skolem_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Generalized function whose value is zero everywhere except at zero
Joseph Fourier. Fourier presented what is now called the Fourier integral theorem in his treatise Théorie analytique de la chaleur (1822) in the form: f
Dirac_delta_function
On finding a maximal set of solutions of a system of first-order homogeneous linear PDEs
given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral
Frobenius theorem (differential topology)
Frobenius_theorem_(differential_topology)
Branch of ordinary differential equations
defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (1883), gives a canonical form
Floquet_theory
Property of differential equations describing physical phenomena
There are many results on this topic. For example, the Cauchy–Kowalevski theorem for Cauchy initial value problems essentially states that if the terms
Well-posed_problem
Equations with an unknown function under an integral sign
y(t)=g(t)+({\mathcal {V}}y)(t)} can be described by the following uniqueness and existence theorem. Theorem—Let K ∈ C ( D ) {\displaystyle K\in C(D)} and let R {\displaystyle
Integral_equation
axiom of choice. This example can be extended into a general theorem about the existence of discontinuous linear maps on any infinite-dimensional normed
Discontinuous_linear_map
Mathematical theorem
The mountain pass theorem is an existence theorem from the calculus of variations, originally due to Antonio Ambrosetti and Paul Rabinowitz. Given certain
Mountain_pass_theorem
Set of real numbers that is not Lebesgue measurable
Lebesgue measurable, found by Giuseppe Vitali in 1905. The Vitali theorem is the existence theorem that there are such sets. Each Vitali set is uncountable, and
Vitali_set
Determinant of the matrix of first derivatives of a set of functions
Roth used this result about generalized Wronskians in his proof of Roth's theorem. For more general conditions under which the converse is valid see Wolsson
Wronskian
Partial differential equation
replaced by a positive number, then the existence theorem discussed in the following section would become a theorem which produces a Ricci flow that moves
Ricci_flow
Approach to finding numerical solutions of ordinary differential equations
{\displaystyle t_{0}} to t 0 + h {\displaystyle t_{0}+h} and apply the fundamental theorem of calculus to get: y ( t 0 + h ) − y ( t 0 ) = ∫ t 0 t 0 + h f ( t , y
Euler_method
Japanese mathematician
1960) was a Japanese mathematician, best known for proving the Takagi existence theorem in class field theory. The Blancmange curve, the graph of a nowhere-differentiable
Teiji_Takagi
Bounded sequence in finite-dimensional Euclidean space has a convergent subsequence
In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result
Bolzano–Weierstrass_theorem
Type of mathematical space
and minima, and major results such as the Arzelà–Ascoli theorem and the Peano existence theorem depend on compactness. In the 19th century, several disparate
Compact_space
Numerical method for solving physical or engineering problems
for twice continuously differentiable u {\displaystyle u} (mean value theorem) but may be proved in a distributional sense as well. We define a new operator
Finite_element_method
Differential equation containing derivatives with respect to only one variable
equations. When the hypotheses of the Picard–Lindelöf theorem are satisfied, then local existence and uniqueness can be extended to a global result. More
Ordinary differential equation
Ordinary_differential_equation
Space of all possible states that a system can take
mechanics. The local density of points in such systems obeys Liouville's theorem, and so can be taken as constant. Within the context of a model system
Phase_space
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Type of problem involving ODEs or PDEs
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Boundary_value_problem
Class of numerical techniques
finite element methods. For a n-times differentiable function, by Taylor's theorem the Taylor series expansion is given as f ( x 0 + h ) = f ( x 0 ) + f ′
Finite_difference_method
Type of differential equation
equation, existence and uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness
Partial_differential_equation
Methods of calculating definite integrals
C 1 ( [ a , b ] ) . {\displaystyle f\in C^{1}([a,b]).} The mean value theorem for f , {\displaystyle f,} where x ∈ [ a , b ) , {\displaystyle x\in [a
Numerical_integration
Type of fluid
analytical solutions could be derived, but a rigorous mathematical existence theorem was given for the solution. For time-independent non-Newtonian fluids
Non-Newtonian_fluid
Theorem on extension of bounded linear functionals
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace
Hahn–Banach_theorem
Technique for solving differential equations
the applicability of separation of variables is a result of the spectral theorem. In some cases, separation of variables may not be possible. Separation
Separation_of_variables
Generalisation of the intermediate value theorem
In mathematics, the Poincaré–Miranda theorem is a generalization of intermediate value theorem, from a single function in a single dimension, to n functions
Poincaré–Miranda_theorem
Continuity equation for conservation laws Maxwell's equations Poynting's theorem Acoustic theory Benjamin–Bona–Mahony equation Biharmonic equation Blasius
List of named differential equations
List_of_named_differential_equations
Methods of mathematical approximation
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Perturbation_theory
Initial estimate or framework to the solution of a mathematical problem
results. An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution
Ansatz
Family of implicit and explicit iterative methods
55), ISBN 978-3030709556 (April, 2021). Butcher, J.C. (1985), "The non-existence of ten stage eighth order explicit Runge-Kutta methods", BIT Numerical
Runge–Kutta_methods
Theorem of stationary processes
Wold representation theorem (not to be confused with the Wold theorem that is the discrete-time analog of the Wiener–Khinchin theorem), named after Herman
Wold's_theorem
Class of problems for PDEs
zero means that the function itself is specified. The Cauchy–Kovalevskaya theorem, named in honor of Cauchy and Sofya Kovalevskaya, states: If all the functions
Cauchy_problem
Part of spectral theory
{\displaystyle Df=-f''+qf.} The following is a version of the classical Picard existence theorem for second order differential equations with values in a Banach space
Spectral theory of ordinary differential equations
Spectral_theory_of_ordinary_differential_equations
Type of ordinary differential equation
{\displaystyle 2x^{2}{\frac {d^{2}y}{dx^{2}}}-3x{\frac {dy}{dx}}+y=2\,.} The existence of a constant term is a sufficient condition for an equation to be inhomogeneous
Homogeneous differential equation
Homogeneous_differential_equation
Method for solving continuous operator problems (such as differential equations)
c\|u\|^{2}} for some constant c > 0. {\displaystyle c>0.} By the Lax-Milgram theorem (see weak formulation), these two conditions imply well-posedness of the
Galerkin_method
Group of mathematical theorems
specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among quotients
Isomorphism_theorems
Finite difference method for numerically solving parabolic differential equations
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Crank–Nicolson_method
Differential equations involving stochastic processes
and whether or not it is unique. The following is a typical existence and uniqueness theorem for Itô SDEs taking values in n-dimensional Euclidean space
Stochastic differential equation
Stochastic_differential_equation
Theorem
subsequences to an integrable random variable (or function). It's also an existence theorem for an integrable random variable (or function). There exist a probabilistic
Komlós'_theorem
Type of ordinary differential equation
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Bernoulli differential equation
Bernoulli_differential_equation
Physics problem related to laws of motion and gravity
strictly bounded away from a triple collision. This implies, by Cauchy's existence theorem for differential equations, that there are no complex singularities
Three-body_problem
Technique for solving linear ordinary differential equations
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Reduction_of_order
Australian and American mathematician (born 1975)
Research Award for: his restriction theorems in Fourier analysis, his work on wave maps, his global existence theorems for KdV-type equations, and for his
Terence_Tao
Method for representing and evaluating partial differential equations
divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite
Finite_volume_method
Solution concept of a non-cooperative game
Kakutani fixed-point theorem in his 1950 paper to prove existence of equilibria. His 1951 paper used the simpler Brouwer fixed-point theorem for the same purpose
Nash_equilibrium
Theorems that help decompose a finite group based on prime factors of its order
specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow
Sylow_theorems
Class of ordinary differential equations
problem). As a consequence of the Arzelà–Ascoli theorem, this integral operator is compact and existence of a sequence of eigenvalues αn which converge
Sturm–Liouville_theory
In the study of zero sum games, Glicksberg's theorem (also Glicksberg's existence theorem) is a result that shows certain games have a minimax value. If
Glicksberg's_theorem
Mathematical theorem in complex analysis
In complex analysis, Mittag-Leffler's theorem concerns the existence of meromorphic functions with prescribed poles. Conversely, it can be used to express
Mittag-Leffler's_theorem
Branch of algebraic number theory concerned with abelian extensions
map from L to F. This isomorphism is named the reciprocity map. The existence theorem states that the reciprocity map can be used to give a bijection between
Class_field_theory
Type of artificial neural network architecture
architecture inspired by the Kolmogorov–Arnold representation theorem, also known as the superposition theorem. Unlike traditional multilayer perceptrons (MLPs),
Kolmogorov–Arnold_Networks
Type of boundary condition in mathematics
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Robin_boundary_condition
Theorem on the orders of subgroups
There are partial converses to Lagrange's theorem. For general groups, Cauchy's theorem guarantees the existence of an element, and hence of a cyclic subgroup
Lagrange's theorem (group theory)
Lagrange's_theorem_(group_theory)
Connects non-singular algebraic curves with compact Riemann surfaces
complex projective line with monodromy group PSL(2,11). Belyi's theorem is an existence theorem for Belyi functions, and has subsequently been much used in
Belyi's_theorem
Fixed-point theorem for set-valued functions
proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani's theorem extends this
Kakutani_fixed-point_theorem
Type of constraint on solutions to differential equations
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Dirichlet_boundary_condition
Mathematical use of "there exists"
the universal quantifier is the right adjoint. Existential clause Existence theorem First-order logic Lindström quantifier List of logic symbols – for
Existential_quantification
Philosophical question
The existence of God is a subject of debate in the philosophy of religion and theology. A wide variety of arguments for and against the existence of God
Existence_of_God
Theorem in mathematics
In calculus and real analysis, the mean value theorem (or Lagrange's mean value theorem) is a theorem about differentiable functions, roughly stating
Mean_value_theorem
Partial differential equations with random force terms and coefficients
drastically expanded, and now there exists a large machinery to guarantee local existence for a variety of sub-critical SPDEs. Brownian surface Kardar–Parisi–Zhang
Stochastic partial differential equation
Stochastic_partial_differential_equation
Method of solution for inhomogeneous ODEs
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Method of undetermined coefficients
Method_of_undetermined_coefficients
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Every polynomial has a real or complex root
The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial
Fundamental theorem of algebra
Fundamental_theorem_of_algebra
Mocking catchphrase
describe American economic policy toward China. Existence theorem – Theorem which asserts the existence of an object Occam's razor – Philosophical problem-solving
Assume_a_can_opener
". Computer Science Stack Exchange. Retrieved 21 November 2014. Existence theorem#'Pure' existence results Constructive proof#Non-constructive proofs
Non-constructive algorithm existence proofs
Non-constructive_algorithm_existence_proofs
Plot of a dynamical system's trajectories in phase space
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Phase_portrait
EXISTENCE THEOREM
EXISTENCE THEOREM
Girl/Female
Tamil
Existence
Girl/Female
Indian
Abode, Existence
Girl/Female
Hindu
Existence, Real
Boy/Male
Indian
Existence
Girl/Female
Tamil
Abode, Existence
Boy/Male
Hindu
Existence, Real
Boy/Male
Tamil
Existence, Real
Girl/Female
Hindu, Indian
Existence
Girl/Female
Indian
Abode, Existence
Girl/Female
Tamil
Existence, Real
Girl/Female
Australian
Existence
Boy/Male
Hindu
Existence
Girl/Female
Arabic, Muslim
Existence
Boy/Male
Tamil
Astitva | அஸà¯à®¤à®¿à®¤à¯à®µ
Existence
Astitva | அஸà¯à®¤à®¿à®¤à¯à®µ
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Existence
Girl/Female
Tamil
Existence, Real
Girl/Female
Hindu
Existence, Real
Girl/Female
Tamil
Abode, Existence
Boy/Male
Arabic, Muslim
Life; Existence
Girl/Female
Indian
Existence
EXISTENCE THEOREM
EXISTENCE THEOREM
Male
English
Blessed
Boy/Male
Tamil
Lotus
Girl/Female
Tamil
Raaga or patience
Boy/Male
Indian, Sanskrit
Enemy of Shakra
Girl/Female
Danish, Dutch, German, Swedish
Frenchman; Free Woman
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Superb Jewel
Girl/Female
Tamil
Narnrata | நாரà¯à®¨à¯à®°à®¤à®¾
Humble, Submissive
Girl/Female
Australian, British, English
Name Given to Children that are Born on a Love Day
Boy/Male
Indian
Lucky, Blissful, Witness
Girl/Female
Indian
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
n.
Inherence; inherent existence.
n.
Subsequent existence.
n.
Life; existence.
a.
Having being or existence; existing; being; occurring now; taking place.
n.
Outward existence.
a.
Existing of or by himself,independent of any other being or cause; -- as, God is the only self-existent being.
n.
Existence.
n.
Real being; existence.
a.
Not having existence.
n.
That which exists; a being; a creature; an entity; as, living existences.
n.
Want of being or existence.
a.
Capable of existence.
a.
Having existence.
n.
Existence; being.
n.
Lifetime; mortal existence.
n.
Inherent existence; existence possessed by virtue of a being's own nature, and independent of any other being or cause; -- an attribute peculiar to God.
a.
Causing existence; productive.
n.
The state of existing or being; actual possession of being; continuance in being; as, the existence of body and of soul in union; the separate existence of the soul; immortal existence.
n.
Existence at the same time with another; -- contemporary existence.
n.
Continued or repeated manifestation; occurrence, as of events of any kind; as, the existence of a calamity or of a state of war.