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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1133,
author = {Zbigniew Grande},
title = {On some equations y'(x) = f(x,y(h(x)+g(y(x))))},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {31},
year = {2011},
pages = {173-182},
zbl = {1260.34122},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1133}
}
Zbigniew Grande. On some equations y'(x) = f(x,y(h(x)+g(y(x)))). Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 31 (2011) pp. 173-182. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1133/
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