Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 187-202
Nonlinear evolution equations on Banach space
University of Ottawa, Department of Mathematics and Department of Electrical Engineering, Ottawa, Canada
Received 1 February 1991; Revised 1 May 1991
Copyright © 1991 N. U. Ahmed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper we consider the questions of existence and
uniqueness of solutions of certain semilinear and quasilinear evolution
equations on Banach space. We consider both deterministic and
stochastic systems. The approach is based on semigroup theory and
fixed point theorems. Our results allow the nonlinear perturbations in all
the semilinear problems to be bounded or unbounded with reference to
the base space, thereby increasing the scope for applications to partial
differential equations. Further, quasilinear stochastic evolution equations
seemingly have never been considered in the literature.