Existence result for a class of stochastic quasilinear partial differential equations with non-standard growth

Abstract

In this dissertation, we investigate a very interesting class of quasi-linear stochastic partial differential equations. The main purpose of this article is to prove an existence result for such type of stochastic differential equations with non-standard growth conditions. The main difficulty in the present problem is that the existence cannot be easily retrieved from the well known results under Lipschitz type of growth conditions [42].