非线性Neumann问题正解的存在性

马如云, 陈瑞鹏, 李杰梅

数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 289-300.

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数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 289-300. DOI: 10.12386/A2013sxxb0030
论文

非线性Neumann问题正解的存在性

    马如云1, 陈瑞鹏1,2, 李杰梅1,2
作者信息 +

Existence of Positive Solutions of Nonlinear Neumann Problems

    Ru Yun MA1, Rui Peng CHEN1,2, Jie Mei LI1,2
Author information +
文章历史 +

摘要

研究非线性Neumann 问题(p(t)u')'+q(t)u=f(t, u), t ∈ (0, 1), u'(0)=u'(1)=0,正解的存在性, 其中p, qC[0, 1]满足p > 0, 0 < q < b* in [0, 1], b*为线性问题(p(t)u')'+bu=0, u'(0)=0, u(1)=0的第一特征值. 运用拓扑度理论及Rabinowitz全局分歧定理为上述问题建立了正解的存在性结果.

Abstract

We are concerned with the existence of positive solutions of the nonlinear Neumann problem (p(t)u')'+q(t)u=f(t, u), t ∈ (0, 1), u'(0)=u'(1)=0, where p, qC[0, 1] with p > 0, 0 < q < b* in [0, 1], b* is the first eigenvalue of the Robin problem (p(t)u')'+bu=0, u'(0)=0, u(1)=0. By applying the topological degree theory and global bifurcation techniques, we establish the existence results of positive solutions for above problem.

关键词

存在性 / 特征值 / Neumann问题 / 分歧方法 / 正解

Key words

existence / eigenvalues / Neumann problem / bifurcation methods / positive solutions

引用本文

导出引用
马如云, 陈瑞鹏, 李杰梅. 非线性Neumann问题正解的存在性. 数学学报, 2013, 56(3): 289-300 https://doi.org/10.12386/A2013sxxb0030
Ru Yun MA, Rui Peng CHEN, Jie Mei LI. Existence of Positive Solutions of Nonlinear Neumann Problems. Acta Mathematica Sinica, Chinese Series, 2013, 56(3): 289-300 https://doi.org/10.12386/A2013sxxb0030

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基金

国家自然科学基金资助项目(11061030);国家自然科学天元基金资助项目(11226132);高校基本科研业务费专项资金资助项目(212084)

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