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

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