Nonlinear evolution equations on Banach space

This paper considers the questions of existence and uniqueness of solutions of certain semilinear and quasilinear evolution equations on Banach space. It considers both deterministic and stochastic systems. The approach is based on semigroup theory and fixed point theorems. The present 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.