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

Zbigniew Grande (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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.

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