On a class of abstract damped second order integrodifferential equations. (English) Zbl 1058.34075
The authors deal with the existence of solutions of nonlinear damped second-order integrodifferential equations in a Banach space. To this end, the authors use the theory of strongly continuous cosine families of operators and Schäfer’s fixed-point theorem. Moreover, they discuss as an application a controllability problem for a damped second-order integrodifferential system.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
34G20 | Nonlinear differential equations in abstract spaces |
47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
93B05 | Controllability |