Existence for an elliptic system with nonlinear boundary conditions

In this paper we prove the existence of a weak solution to the following system {Delta(p)u = Delta(q)v = 0 in Omega, vertical bar del u vertical bar(p-2)partial derivative u/partial derivative v = f(x, u) - (alpha+1) K(x)vertical bar u vertical bar(alpha-1) u vertical bar v vertical bar(beta+1) vertical bar f(1) on partial derivative Omega, vertical bar del v vertical bar(q-2)partial derivative u/partial derivative v = g(x, u) - (beta+1) K(x)vertical bar v vertical bar(beta-1) v vertical bar u vertical bar(alpha+1) vertical bar f(1) on partial derivative Omega, where Omega is a bounded domain R-N (N >= 2), f(1), g(1), f, g and K are functions that satisfy some conditions.