Positive solutions of BVPs for third-order discrete nonlinear difference systems
Positive solutions of BVPs for third-order discrete nonlinear difference systems
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DOI：
10.1007/s12190-010-0378-7
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发表时间：
2011-02
影响因子：
2.2
通讯作者：
Rui Zhang
中科院分区：
文献类型：
--
作者：
Rui Zhang
本文讨论了如下系统3：ui(K)+fi(k，u1(K)，u2(K)，…，un(K))=0，k∈[0，T]，i=1，2，…，n，具有Dirichlet边界条件ui(0)=ui(1)=ui(T+3)=0，i=1，2，…，n.利用Leray-Schauder型的非线性变换，得到了上述系统正解的存在性、多解性和不存在性的一些结果.Krasnosel‘skii锥上的不动点定理和Leggett-Williams不动点定理。特别地，证明了在适当的条件下，上述系统有N个正解，其中N为任意整数。
This paper is concerned with the following system3 ui (k)+ fi (k, u1 (k), u2 (k),..., un (k))= 0, k∈[0, T], i= 1, 2,..., n, with the Dirichlet boundary condition ui (0)= ui (1)= ui (T+ 3)= 0, i= 1, 2,..., n.Some results are obtained for the existence, multiplicity and nonexistence of positive solutions to the above system by using nonlinear alternative of Leray-Schauder type, Krasnosel’skii’s fixed point theorem in a cone and Leggett-Williams fixed point theorem. In particular, it proves that the above system has N positive solutions under suitable conditions, where N is an arbitrary integer.