On the nonexistence and uniqueness of positive weak solutions for nonlinear multiparameter elliptic systems involving the (p,q)-Laplacian

摘要

The paper deal with the nonexistence and uniqueness of positive weak solutions for the nonlinear multiparameter elliptic system -(DELTA)_(p)u velence (lambda)_(1) f(v) + (mu)_(1) h(u), x E OMEGA, -(DELTA)_(q)v velence (lambda)_(2) g(u) + (mu)_(2) k(v), x E OMEGA, u velence 0 velence v, x E (partial deriv)(OMEGA), where OMEGA is a bounded domain in R~(N) (N > 1) with smooth boundary (partial deriv)(OMEGA), (DELTA)_(p) denotes the p-Laplacian operator defined by (DELTA)_(p)z velence div (|(nabla)z|~(p-2)(nabla)_(z)), p > 1, f, g, h, k : [0, infinity) -> [0, infinity), and (lambda)_(1), (lambda)_(2), (mu)_(1), (mu)_(2) are positive parameters. A uniqueness and nonexistence result is obtained by applying the comparison principles for the p-Laplacian.