Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 3, Pages 187-202
doi:10.1155/S1048953391000151
Abstract
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.