Displaying similar documents to “Picard's Demonstration of the General Theorem upon the Existence of Integrals of Ordinary Differential Equations.”

Integrals of Frullani type and the method of brackets

Sergio Bravo, Ivan Gonzalez, Karen Kohl, Victor H. Moll (2017)

Open Mathematics

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The method of brackets is a collection of heuristic rules, some of which have being made rigorous, that provide a flexible, direct method for the evaluation of definite integrals. The present work uses this method to establish classical formulas due to Frullani which provide values of a specific family of integrals. Some generalizations are established.

Differential inclusions and multivalued integrals

Kinga Cichoń, Mieczysław Cichoń, Bianca Satco (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is...