ON STRONGLY QUASILINEAR DEGENERATE ELLIPTIC SYSTEMS WITH WEAK MONOTONICITY AND NONLINEAR PHYSICAL DATA

This work is devoted to studying the quasilinear elliptic system $$\begin{aligned} -div ~ a(x,u,Du) + \vert u\vert ^{p-2} u +b(x,u,Du)=v(x)+f(x,u)+div ~g(x,u) \end{aligned}$$ on a bounded open domain of $$\mathbb {R}^n$$ with homogeneous Dirichlet boundary conditions. We show that there weak solution this under regularity, growth, and coercivity conditions for a, but only very moderate monotonicity assumptions. prove existence result by using Galerkin’s approximation theory Young measures.