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

• Autorzy: Zbigniew Grande
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 26B05: Continuity and differentiation questions
• 39B12: Iteration theory, iterative and composite equations
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2011
• Tom: 31
• Numer: 2
• Strony: 173-182

Daty

wydano

2011

otrzymano

2011-01-17

Twórcy

autor

Zbigniew Grande

• 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.

Identyfikatory

DOI

10.7151/dmdico.1133