Abstract
In this article, we study the existence results of large positive weak solution for nonlinear system with singular weights (1.4), where Omega is a bounded domain of Rn with boundary partial derivative Omega, 0 is an element of Omega, 1 < p, q < n, 0 <= r < n-p/p, 0 <= s < n-q/q, and Lambda(p)u = vertical bar u vertical bar(p-2)u, rho(p), rho(q), lambda, mu, gamma, delta are positive constants and a, b are weight functions. We prove the existence of a large positive weak solutions for mappings. lambda, mu large when lim(x ->+infinity) f(1/p-1) (M(g(x))(1/q-1))/x = 0, for every M > 0. Here, there is no any sign-changing conditions on a or b. The proof of the main results is based on the sub-supersolutions method. Application and concluding remark are provided to demonstrate the effectiveness of our results.