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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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
State of being real
mathematical object matching a certain description exists is called an existence theorem. Metaphysicians of mathematics investigate whether mathematical objects
Existence
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
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
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
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
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
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
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
cohomology Hasse norm theorem Herbrand quotient Hilbert class field Kronecker–Weber theorem Local class field theory Takagi existence theorem Tate cohomology
Class_formation
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
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
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
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
Statement in mathematical combinatorics
In combinatorics, Ramsey's theorem, in one of its graph-theoretic forms, states that one will find monochromatic cliques in any edge labelling (with colours)
Ramsey's_theorem
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
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
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
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
". 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
choice of very ample line bundle L {\displaystyle {\mathcal {L}}} . It is a theorem of Grothendieck's that the functors Q u o t E / X / S Φ , L {\displaystyle
Quot_scheme
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
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
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
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 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
Every simple polygon with more than three vertices has at least two ears
polygon without introducing any crossings. The two ears theorem is equivalent to the existence of polygon triangulations. It is frequently attributed to
Two_ears_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
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
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
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
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 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
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
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
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
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
Black hole conjecture
trapped surface, sometimes referred as the Schoen–Yau black hole existence theorem and more recently in 2023 using Mikhael Gromov's cube inequality some
Hoop_conjecture
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
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
Mathematical method
functional analysis, a branch of mathematics, a selection theorem is a theorem that guarantees the existence of a single-valued selection function from a given
Selection_theorem
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
American mathematician (born 1937)
of the Riemann-Roch theorem. The theory of abstract varieties, as Mumford showed, can be applied to provide an existence theorem for moduli spaces of
David_Mumford
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
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
Provability logic
Löb's theorem can be proved within normal modal logic using only some basic rules about the provability operator (the K4 system) plus the existence of modal
Löb's_theorem
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
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
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
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 relating the number of edges, vertices and faces of a polyhedron
{\displaystyle p_{i}} all obey the equation that Eberhard's theorem requires them to obey. The existence of these polyhedra shows that, for these three assignments
Eberhard's_theorem
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
Equation involving both integrals and derivatives of a function
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Integro-differential_equation
Theorem
principle. Carl Ludwig Siegel published his lemma in 1929. It is a pure existence theorem for a system of linear equations. Siegel's lemma has been refined
Siegel's_lemma
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
Technique for solving differential equations
Delay Solution Existence and uniqueness Well-posed problem Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kovalevskaya
Integrating_factor
Existence theorem for economical additive bases of every order
additive number theory, an area of mathematics, the Erdős–Tetali theorem is an existence theorem concerning economical additive bases of every order. More specifically
Erdős–Tetali_theorem
Partial differential equation with nonlinear terms
of the Calabi conjecture was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the Navier–Stokes
Nonlinear partial differential equation
Nonlinear_partial_differential_equation
codes in his construction of strongly explicit asymptotically good code. Theorem: Let ε > 0. {\displaystyle \varepsilon >0.} For a large enough k {\displaystyle
Wozencraft_ensemble
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
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
Boy/Male
Tamil
Existence, Real
Girl/Female
Tamil
Existence
Girl/Female
Australian
Existence
Girl/Female
Hindu, Indian
Existence
Boy/Male
Hindu
Existence
Girl/Female
Tamil
Abode, Existence
Girl/Female
Indian
Existence
Boy/Male
Arabic, Muslim
Life; Existence
Girl/Female
Indian
Abode, Existence
Girl/Female
Tamil
Existence, Real
Boy/Male
Indian
Existence
Girl/Female
Hindu
Existence, Real
Girl/Female
Indian
Abode, Existence
Girl/Female
Hindu
Existence, Real
Girl/Female
Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Existence
Boy/Male
Hindu
Existence, Real
Girl/Female
Tamil
Existence, Real
Boy/Male
Tamil
Astitva | அஸà¯à®¤à®¿à®¤à¯à®µ
Existence
Astitva | அஸà¯à®¤à®¿à®¤à¯à®µ
Girl/Female
Tamil
Abode, Existence
Girl/Female
Arabic, Muslim
Existence
EXISTENCE THEOREM
EXISTENCE THEOREM
Boy/Male
Indian, Modern
Inner Soul
Boy/Male
American, Australian, British, Christian, English, German, Greek, Jamaican
Son of Otto; Wealthy
Surname or Lastname
English
English : variant of Foulsham, a habitational name from Foulsham in Norfolk, so named from the Old English personal name Fugol + hÄm ‘homestead’.
Girl/Female
Muslim
Movement, Motion
Boy/Male
Indian, Punjabi, Sikh
Talking Support of God
Girl/Female
Hindu
Name of a Raga
Boy/Male
Indian, Punjabi, Sikh
Brave with Good Sleep
Boy/Male
German Latin
Abbreviation of Alfonso.
Boy/Male
American, Anglo, Australian, British, Danish, English, French, German, Norse, Norwegian, Scandinavian, Swedish, Swiss
Leader of the Army; Army Ruler; Army; Warrior; To Rule
Girl/Female
Hindu, Indian
Vitality
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
EXISTENCE THEOREM
a.
Having being or existence; existing; being; occurring now; taking place.
n.
Lifetime; mortal existence.
n.
Want of being or existence.
n.
Subsequent existence.
n.
Existence; being.
a.
Having 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.
n.
Continued or repeated manifestation; occurrence, as of events of any kind; as, the existence of a calamity or of a state of war.
a.
Not having existence.
n.
Existence at the same time with another; -- contemporary existence.
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.
n.
Inherence; inherent existence.
n.
Outward existence.
a.
Capable of existence.
a.
Existing of or by himself,independent of any other being or cause; -- as, God is the only self-existent being.
n.
Real being; existence.
a.
Causing existence; productive.
n.
Life; existence.
n.
That which exists; a being; a creature; an entity; as, living existences.