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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.
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
173-182
Opis fizyczny
Daty
wydano
2011
otrzymano
2011-01-17
Twórcy
autor
- Institute of Mathematics, Kazimierz Wielki University, Plac Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
Bibliografia
- [1] A.M. Bruckner, Differentiation of real functions, Lectures Notes in Math. 659, Springer-Verlag, Berlin, 1978.
- [2] Z. Grande, A theorem about Carathéodory's superposition, Math. Slovaca 42 (1992), 443-449.
- [3] Z. Grande, When derivatives of solutions of Cauchy's problem are (S)-continuous?, Tatra Mt. Math. Publ. 34 (2006), 173-177.
- [4] W. Li and S.S. Cheng, A Picard theorem for iterative differential equations, Demonstratio Math. 42 (2) 2009, 371-380.
- [5] B.S. Thomson, Real Functions, Lectures Notes in Math., Vol. 1170, Springer-Verlag, Berlin, 1980.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1133