Differential and Integral Equations

Existence of solutions of nonlinear functional integro-differential equations in Banach spaces

Ki Sik Ha, Byoung Jae Jin, and Ki-Yeon Shin

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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.

Article information

Source
Differential Integral Equations, Volume 8, Number 3 (1995), 553-566.

Dates
First available in Project Euclid: 23 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369316505

Mathematical Reviews number (MathSciNet)
MR1306574

Zentralblatt MATH identifier
0813.34065

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 47N20: Applications to differential and integral equations

Citation

Ha, Ki Sik; Shin, Ki-Yeon; Jin, Byoung Jae. Existence of solutions of nonlinear functional integro-differential equations in Banach spaces. Differential Integral Equations 8 (1995), no. 3, 553--566. https://projecteuclid.org/euclid.die/1369316505


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