广义p-Laplace边值问题正解的存在性与多解性

  利用锥上的不动点理论讨论一类含参广义p-Laplace 边值问题正解的存在性与多解性,给出了参数λ的显式开区间。已有文献在多解性研究中,通常要求非线性项在正半轴恒正。本文改进这一基本假设条件,允许非线性项在正半轴的某些子集上恒为零。

The Existence and Multiplicity of Positive Solutions of Generalized p-Laplacian Boundary Value Problems

A generalized p-Laplacian boundary value problem with a parameter is concerned. By using the fixed-point theorem in cones, some results of existence and multiplicity of positive solutions for the problem are established with the parameter belonging to corresponding explicit intervals. In the existed literatures about multiplicity of positive solutions, the nonlinear terms are usually required to be positive for all positive real numbers. This condition is relaxed in the present paper, more precisely, the nonlinear terms can vanish on some subset.