On some equations y'(x) = f(x,y(h(x)+g(y(x))))

Zbigniew Grande

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Title

On some equations y'(x) = f(x,y(h(x)+g(y(x))))

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Affiliations

Institute of Mathematics, Kazimierz Wielki University, Plac Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Abstract

In [4] W. Li and S.S. Cheng prove a Picard type existence and uniqueness theorem for iterative differential equations of the form y'(x) = f(x,y(h(x)+g(y(x)))). In this article I show some analogue of this result for a larger class of functions f (also discontinuous), in which a unique differentiable solution of considered Cauchy's problem is obtained.

Keywords

ENG

iterative differential equation, existence and uniqueness theorem, Picard approximation, derivative, (S)-continuity, (S)-path continuity

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Z. Grande, When derivatives of solutions of Cauchy's problem are (S)-continuous?, Tatra Mt. Math. Publ. 34 (2006), 173-177.
W. Li and S.S. Cheng, A Picard theorem for iterative differential equations, Demonstratio Math. 42 (2) 2009, 371-380.
B.S. Thomson, Real Functions, Lectures Notes in Math., Vol. 1170, Springer-Verlag, Berlin, 1980.

Title

On some equations y'(x) = f(x,y(h(x)+g(y(x))))

Affiliations

Abstract

Keywords

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