Existence results for some elliptic systems with perturbed gradient

Abstract

In this paper, we consider the existence of weak solutions for some quasilinear elliptic problems with perturbed gradient under homogeneous Dirichlet boundary conditions. We apply the Galerkin approximation and the convergence in term of Young measure combined with the theory of Sobolev spaces to obtain the existence of at least one weak solution $u\in W_{0}^{1,p}(\Omega;\mathbb{R}^{m})$.