Differential and Integral Equations
- Differential Integral Equations
- Volume 8, Number 3 (1995), 553-566.
Existence of solutions of nonlinear functional integro-differential equations in Banach spaces
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.
Differential Integral Equations, Volume 8, Number 3 (1995), 553-566.
First available in Project Euclid: 23 May 2013
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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