Abstract
In this article, we study the existence of positive weak solutions for a class of weighted (p,q)-Laplacian nonlinear system { -Delta(P,p)u = lambda a(x) f(v) in Omega, -Delta(Q,q)v = lambda b(x) g(u) in Omega, u = v = 0 on partial derivative Omega, where Delta(P,p) with p > 1 and P = P(x) is a weight function, denotes the weighted p-Laplacian defined by Delta(P,p)u equivalent to div[P(x)vertical bar del u vertical bar(p-2)del u], lambda is a positive parameter, a(x), b(x) are weight functions and Omega subset of R-N is a bounded domain with smooth boundary partial derivative Omega. We provve existence of a large positive weak solution for lambda large when lim f1/p-1 (M(g(x)) 1/q-1)/x =0, for every M > 0. x -> +infinity
In particular, we do not assume any sign-changing conditions on a(x) or b(x). We use the method of sub-supersolutions to establish our results.