A Remark on the Existence of Positive Solution for a Class of (p,q)-Laplacian Nonlinear System with Multiple Parameters and Sign-Changing Weight

摘要

The paper deal with the existence of positive solution for the following (p,q)-Laplacian nonlinear system{-△pu=a(x)(α1f(v)+β1h(u)),x∈Ω,-△qv=b(x)(α2g(u)+β2k(v)),x∈Ω,u=v=0,x∈（з）Ω,where △p denotes the p-Laplacian operator defined by △pZ =div (|▽z|p-2▽Z),p ＞ 1,α1,α2,β1,β2 are positive parameters and Ω is a bounded domain in RN(N ＞ 1)with smooth boundary （ε）Ω.Here a(x) and b(x) are C1 sign-changing functions that maybe negative near the boundary and f,g,h,k are C1 nondecreasing functions such that f,g,h,k:[0,∞)→ [0,∞);f(s),g(s),h(s),k(s) ＞ 0;s ＞ 0 and lim（x→∞) f(Mg(x)1/(q-1))/(xp-1) =0 for every M ＞ 0.We discuss the existence of positive solution when f,g,h,k,a(x) and b(x) satisfy certain additional conditions.We use the method of sub-super solutions to establish our results.