半正Neumann边值问题的解和正解的存在性与多解性

Existence andMultiplicity of Solutions and Positive Solutions for Sem ipositive Neumann Boundary Value Problem s

摘要: 利用锥拉伸与锥压缩型的Krasnosel skii不动点定理考察了一类非线性Neumann边值问题的解和正解, 其中允许非线性项有非正的下界.研究表明,只要非线性项在某些有界集上的最大高度和最小高度是适当的,这个问题便具有n(n为任意自然数)个解或者正解.
- 存在性 /
- 多解性 /
- 二阶常微分方程 /
- Neumann边值问题 /
- 解和正解
Abstract: By using cone expansion-compression fixed point theorem, the solutions and positive solutionswere studied for the nonlinearNeumann boundary value problem, where the nonlinear term was allowed to have a nonpositive lowerbound. It is shown that the problem hasnsolutions orpositive solutions provided themaximum andminimum heights of the nonlinear terms are appropriate on some bounded sets, wherenis a naturalnumber
- existence /
- multiplicity of solutions /
- second order differential equation /
- Neumann boundary value problem /
- positive solution

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