半正Neumann边值问题的解和正解的存在性与多解性

Existence and Multip licity of Solutions and Positive Solutions for Semipositive Neumann Boundary Value Problems

利用锥拉伸与锥压缩型的Krasnoselskii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.

By using cone expansion-compression fixed point theorem, the solutions and positive solutions were studied for the nonlinear Neumarm boundary value problem, where the nonlinear term was allowed to have a nonpositive lower bound. It is shown that the problem has n solutions or positive solutions provided the maximum and minimum heights of the nonlinear terms are appropriate on some bounded sets, where n is a natural number.