Hasnae El Hammar, Said Ait Temghart, Chakir Allalou, Said Melliani

Existence of Solutions for Some Elliptic Systems with Perturbed Gradient

abstract:
In this paper, we study the existence of weak solutions for some quasilinear elliptic problems with perturbed gradients under homogeneous Dirichlet boundary conditions. Using the approximate Galerkin method and combining the convergence in terms of Young measure and the theory of Sobolev spaces, we can prove that there is at least one weak solution $u\in W_{0}^{1,p(x)}(\Omega;\mathbb{R}^{m})$ to the problem treated.

Mathematics Subject Classification: 35J60, 35D05, 76A05

Key words and phrases: Quasilinear elliptic systems, approximate Galerkin method, Young measures