一维p-Laplacian半正问题的变号解(英文)

Sign-changing Solutions of the One-dimensional p-Laplacian Semi-positone Problems

本文研究了一维p-Laplacian问题(|u′(t)|^(p-2)u′(t))′+λf/(u(t))=0,0<t<1,u(0)-αu′(0)=0,u(1)+βu′(1)=0,(P)变号解的存在性,其中p∈(1,2],λ>0,α≥0,β≥0,f:R→R足够光滑,f(0)<0.证明了存在λ~*∈(0,∞)使得当λ∈(0,λ~*)时,问题(P)有唯一确切的满足特定结点性质的解.主要结果基于时间映像分析法.

In this paper we investigate the existence of the sign-changing solutions of the one-dimensional p-Laplacian（｜u′（t）｜^（p-2）u′（t））′ ＋ λf/（u（t）） = 0,0t1,u（0）-αu′（0） = 0,u（1） ＋ βu′（1） = 0,（P）where p ∈（1,2],λ 0,α≥0,β≥0,f：R→ R smooth enough,f（0） 0.We also obtain that there exists λ~＊ ∈（0,∞） such that（P） has exactly one solution having specified nodal properties for λ∈（0,λ~＊）.Our main results are based on time-map method.