Electron. J. Diff. Equ., Vol. 2014 (2014), No. 07, pp. 1-10.

Existence of solutions for iterative differential equations

Pingping Zhang, Xiaobing Gong

The presence of self-mapping increases the difficulty in proving the existence of solutions for general iterative differential equation. In this article we provide conditions for the existence of solutions for the initial value problem, in which the conditions are natural and easily verifiable. We generalize the relevant results and point out the mistake in some references.

Submitted August 21, 2013. Published January 7, 2014.
Math Subject Classifications: 34A12, 39B12, 47H10.
Key Words: Existence; nonautonomous; iteration differential equation; Schauder's fixed point theorem.

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Pingping Zhang
Department of Mathematics and Information Science
Binzhou University
Shandong 256603, China
email: zhangpingpingmath@163.com
Xiaobing Gong
Department of Mathematics
Neijiang Normal University
Sichuan 641100, China
email: xbgong@163.com

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