the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which...

Peano's existence theorem. Peano's theorem requires that the right-hand side of the differential equation be continuous, while Carathéodory's theorem shows...

Giuseppe Peano (/piˈɑːnoʊ/; Italian: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of...

Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem is named after Émile Picard, Ernst Lindelöf...

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...

hypotheses of the incompleteness theorem. Thus by the first incompleteness theorem, Peano Arithmetic is not complete. The theorem gives an explicit example of...

{\displaystyle T\vdash s} . The model existence theorem and its proof can be formalized in the framework of Peano arithmetic. Precisely, we can systematically...

the Cauchy–Kovalevskaya theorem (also written as the Cauchy–Kowalevski theorem) is the main local existence and uniqueness theorem for analytic partial differential...

equations. When the hypotheses of the Picard–Lindelöf theorem are satisfied, then local existence and uniqueness can be extended to a global result. More...

In mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural...

Bolzano–Weierstrass theorem from spaces of geometrical points to spaces of functions. The Arzelà–Ascoli theorem and the Peano existence theorem exemplify applications...

consequence of Kruskal's theorem and Kőnig's lemma. For each n, Peano arithmetic can prove that P ( n ) {\displaystyle P(n)} is true, but Peano arithmetic cannot...

In mathematical logic, Löb's theorem states that in Peano arithmetic (PA) (or any formal system including PA), for any formula P, if it is provable in...

subjects of interest. For first order initial value problems, the Peano existence theorem gives one set of circumstances in which a solution exists. Given...

right-hand side of the differential equation is continuous. Hence, the Peano existence theorem applies so there is a (possibly non-unique) solution. To see why...

existence of a Peano curve such that at each point of the real line at least one of its components is differentiable. The Hahn–Mazurkiewicz theorem is...

common misconception is that W = 0 everywhere implies linear dependence. Peano (1889) pointed out that the functions x2 and |x| · x have continuous derivatives...

the Peano existence theorem, give sufficient conditions for solutions to exist without necessarily being unique, which can allow for the existence of singular...

(differential equations) Liénard's theorem (dynamical systems) Markus−Yamabe theorem (dynamical systems) Peano existence theorem (ordinary differential equations)...

In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf...

zero means that the function itself is specified. The Cauchy–Kowalevski theorem states that If all the functions F i {\displaystyle F_{i}} are analytic...

system of Peano arithmetic plus the statement "Peano arithmetic is consistent" (which, per the incompleteness theorem, cannot be proved in Peano arithmetic)...

12 September 2010. Hörmander 1983, p. 56. Rudin 1991, Theorem 6.25. Stein & Weiss 1971, Theorem 1.18. Rudin 1991, §II.6.31. More generally, one only needs...

Solution Existence and uniqueness Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kowalevski theorem General topics...

Solution Existence and uniqueness Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kowalevski theorem General topics...

equation, existence and uniqueness theorems are usually important organizational principles. In many introductory textbooks, the role of existence and uniqueness...

the usual result guaranteeing the local existence of a unique solution does not apply. The Peano existence theorem however proves that even for f merely...

Solution Existence and uniqueness Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kowalevski theorem General topics...

natural numbers represent 1 in various ways. In Giuseppe Peano's original formulation of the Peano axioms, a set of postulates to define the natural numbers...

Solution Existence and uniqueness Picard–Lindelöf theorem Peano existence theorem Carathéodory's existence theorem Cauchy–Kowalevski theorem General topics...