一维P-Laplacian方程正解的三解定理

AN THEOREM ABOUT TRIPLE POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL P-LAPLACIAN EQUATIONS

本文应用Leggett-Williams不动点定理,研究具有P-Laplacian算子的非线性边值问题(φ(u′))′+α(t)f(u)=0,αφ(u(0))-βφ(u′(0))=0,γφ(u(1))+δφ(u′(1)) =0正解的存在性,其中φ(s):=|s|^(p-2)s,p>1,我们建立了该问题至少存在三个正解的充分条件。

By means of the Leggtt-Williams fixed-point theorem in cones, we study the existence of positive solutions for the nonlinear p-Laplacian boundary value problem, (ψ(u'))' + α(t)f(u) = 0, αψ(u(0)) -β ψ(u'(0)) = 0, γψ(u(1)) +δψ(u'(1)) = 0, where ψ(s) := |s|P-2s, p > 1. Sufficient conditions are established which guarantee the existence of at least three positive solutions of this problem.