Existence of Positive Solutions for a Class of Kirchhoff Type Systems

摘要

In this paper,we are interested in the existence of positive solutions for the Kirchhoff type problems ｛-(a1 + b1M1(∫Ω |▽u|pdx))△pu =λf(u,v),in Ω,-(a2 + b2M2(∫Ω |▽v|qdx))△qv =λg(u,v),in Ω,u =v =0,on (e)Ω,where 1 ＜ p,q ＜ N,Mi:R+0 → R+ (i =1,2) are continuous and increasing functions.λ isa parameter,f,g ∈ C1((0,∞) × (0,∞)) × C([0,∞) × [0,∞)) are monotone functions such that fs,ft,gs,gt ≥ 0,and f(0,0) ＜ 0,g(0,0) ＜ 0 (semipositone).Our proof is based on the sub-and super-solutions techniques.