The existence of countably many positive solutions for nonlinear singular m-point boundary value problems
The existence of countably many positive solutions for nonlinear singular m-point boundary value problems
复制标题
DOI：
10.1016/j.cam.2007.02.020
复制
发表时间：
2008-04
影响因子：
2.4
通讯作者：
Sihua Liang;Jihui Zhang
中科院分区：
文献类型：
--
作者：
Sihua Liang;Jihui Zhang
本文研究了非线性奇异边值问题在边值条件下可数个正解的存在性：其中 ψ:R→R 为增同胚和正同态，ψ(0)=0,ψi∈(0,1)，其中 0<ψ1<ψ2<⋯<ψm-2<1 且 αi,β 满足αi,βi∈[0,+∞),0<Σi=1m-2αi<1,0<Σi=1m-2βi<1, f∈C([0,+∞),[0,+∞)), a:[0,1]→[0,+∞) 并且在 [0,12) 中有可数个奇点。我们利用不动点指数理论和新的锥体不动点定理证明了存在可数个正解。
In this paper, we study the existence of countably many positive solutions for nonlinear singular boundary value problemsubject to the boundary value conditions:where ϕ:R→R is an increasing homeomorphism and positive homomorphism and ϕ(0)=0,ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξm-2<1 and αi,βisatisfy αi,βi∈[0,+∞),0<∑i=1m-2αi<1,0<∑i=1m-2βi<1, f∈C([0,+∞),[0,+∞)), a:[0,1]→[0,+∞) and has countably many singularities in [0,12). We show that there exist countably many positive solutions by using the fixed-point index theory and a new fixed-point theorem in cones.