Existence of multiple positive solutions for one-dimensional p-Laplacian
Existence of multiple positive solutions for one-dimensional p-Laplacian
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DOI：
10.1016/j.jmaa.2005.09.085
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发表时间：
2006-03
影响因子：
1.3
通讯作者：
Youyu Wang;Chengmin Hou
中科院分区：
文献类型：
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作者：
Youyu Wang;Chengmin Hou
本文考虑一维p-拉普拉斯算子的多点边值问题，其边值条件为：其中，ϕp(s)=|s|p−2s, p |, ξi∈(0,1)，且0<ξ1<ξ2<⋯<ξn−2<1，且ai， bis满足ai，bi∈[0,∞],0<∑i=1n−2ai<1,∑i=1n−2bi<1。利用锥上算子的不动点定理，给出了上述边值问题存在多个（至少三个）正解的充分条件。
In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian subject to the boundary value conditions: where ϕp(s)=|s|p−2s, p>1, ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξn−2<1, and ai,bisatisfy ai,bi∈[0,∞], 0<∑i=1n−2ai<1, and ∑i=1n−2bi<1. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.