EXISTENCE OF SOLUTIONS FOR A DEGENERATE QUASILINEAR ELLIPTIC SYSTEM IN BOUNDED DOMAIN

Using variational methods, we study the existence of weak solutions for the degenerate quasilinear elliptic system {-div(h(1)(x)vertical bar del u vertical bar(p-2)del u) = F-u(x, u, v) in Omega, -div(h(2)(x)vertical bar del u vertical bar(p-2)del u) = F-v(x, u, v) in Omega, u = v = 0 on partial derivative Omega, where Omega subset of RN is a smooth bounded domain, del F = (F-u, F-v) stands for the gradient of C-1-function F : Omega x R-2 -> R, the weights h, i = 1,2 are allowed to vanish somewhere, the primitive F(x, u, v) is intimately related to the first eigenvalue of a corresponding quasilinear system.