Abstract
We study the maximum principle and existence of positive solutions for the nonlinear system
-Delta(p),(P)u - a(x)vertical bar u vertical bar(p-2)u + b(x)vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta)v + f in Omega, -Delta(Q),(q)v = c(x)vertical bar u vertical bar(alpha)vertical bar v vertical bar(beta)u + d(x)vertical bar v vertical bar(q-2)v + g in Omega, u = v = 0 on partial derivative Omega,
where the degenerate p-Laplacian defined as Delta(p,P)u = div[P(x)vertical bar del u vertical bar(p-2)del u]. We give necessary and sufficient conditions for having the maximum principle for this system and then we prove the existence of positive solutions for the same system by using an approximation method.