Nonlinear discrete Sturm–Liouville problems
Nonlinear discrete Sturm–Liouville problems
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DOI：
10.1016/j.jmaa.2005.01.032
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发表时间：
2005-08
影响因子：
1.3
通讯作者：
Jesús F. Rodríguez
中科院分区：
文献类型：
--
作者：
Jesús F. Rodríguez
本文研究了以参数λ为相关线性问题的特征值的形式的非线性边值问题，即存在满足边界条件的非平凡函数u，且t在{a+1，a+2，…中，b+1}。我们建立了这类问题可解的充分条件。此外，在非线性“小”的情况下，我们给出了非线性问题的解与线性问题的特征函数之间的关系的定性分析。
In this paper we study nonlinear boundary value problems of the form subject to The parameter λ is an eigenvalue of the associated linear problem; that is, there is a nontrivial function u that satisfies the boundary conditions and also for t in {a+1,a+2,…,b+1}. We establish sufficient conditions for the solvability of such problems. In addition, in those cases where the nonlinearity is “small,” we provide a qualitative analysis of the relation between solutions of the nonlinear problem and eigenfunctions of the linear one.