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1995 Existence of solutions of nonlinear functional integro-differential equations in Banach spaces
Ki Sik Ha, Byoung Jae Jin, Ki-Yeon Shin
Differential Integral Equations 8(3): 553-566 (1995).

Abstract

We consider the existence of generalized solutions of a nonlinear functional integro-differential equation of type $$ x'(t)+A(t, x_t)x(t)\ni G(t,x_t,\int^t_0k(t,s,x_s)ds),\quad t\in [0,T),\quad x_0=\phi $$ in general Banach spaces. Our study is performed by means of the concept of the Method of Lines and well known Banach fixed point theorems. We extend the results of Kartsatos and Parrott, Tanaka to an abstract nonlinear integro-differential equation.

Citation

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Ki Sik Ha. Byoung Jae Jin. Ki-Yeon Shin. "Existence of solutions of nonlinear functional integro-differential equations in Banach spaces." Differential Integral Equations 8 (3) 553 - 566, 1995.

Information

Published: 1995
First available in Project Euclid: 23 May 2013

zbMATH: 0813.34065
MathSciNet: MR1306574

Subjects:
Primary: 45K05
Secondary: 34K30, 47N20

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 3 • 1995
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