Solvability of Nonlinear Elliptic Type Equation With Two Unrelated Non standard Growths

Abstract

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths in a bounded domain $\Omega \subset {\mathbb{R}}^n$. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.