Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 187-202

Nonlinear evolution equations on Banach space

N. U. Ahmed

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.