摘要
We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>1, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0<ξ1<ξ2< ··· <ξm-2<1,0 < Σm-2 i=1 ki<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics.
We study the following nonlinear m/point p-Laplacian boundary value problem with non-homogenous condition：（Фp（u＇）＇＋f（t,u,u＇）=0,0〈t〈1,u＇（0）=0,u（1）-∑i=1 m-2kiu（ξi）=λ,where Фp（s）=│s│^p-2s,p〉1,λ〉0,ki≥0（i=1,2,…,m-2）,0〈ξ1〈ξ2〈…〈ξm-2〈1,0〈∑i=1 m-2ki〈1.Under sufficient conditions, we show that there exists a positive number λ＊such that the problem has at least one positive solution for 0 〈λ〈λ＊and no solution for〉λ 〉 λ＊. The proof is based on the Schauder fixed point theorem and upper-lower technics.
