奇异非线性边值问题的经典Agarwal-O'Regan方法

姚庆六

数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 903-918.

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PDF(606 KB)
数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 903-918. DOI: 10.12386/A2012sxxb0087
论文

奇异非线性边值问题的经典Agarwal-O'Regan方法

    姚庆六
作者信息 +

Classical Agarwal-O'Regan Method on Singular Nonlinear Boundary Value Problems

    Qing Liu YAO
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文章历史 +

摘要

改进了奇异非线性边值问题的经典Agarwal-O'Regan方法. 利用这个改进的方法建立了奇异非线性(p, n-p)共轭边值问题正解的局部存在性与多解性, 其中允许非线性项关于时间和空间变元同时奇异.主要工具是锥拉伸与锥压缩型的Guo-Krasnosel'skii不动点定理和精确先验估计技巧. 特别的, 考察了非自治奇异非线性二阶、三阶、四阶共轭边值问题.

Abstract

The classical Agarwal-O'Regan method on singular nonlinear boundary value problems is improved.The local existence and multiplicity of positive solutions are established for the singular nonlinear(p,n-p)conjugate boundary value problems by applying this improved method,where the nonlinear term is allowed to be singular with respect to both the time and space variables.Main tools are the Guo Krasnosel'skii fixed point theorem of cone expansion-compression type and the exact apriori estimation technique.Particularly,the nonautonomous singular nonlinear second,third,fourth-order conjugate boundary value problems are considered.

关键词

奇异常微分方程 / 边值问题 / 正解 / 存在性 / 多解性

Key words

singular ordinary Differential equation / boundary value problem / positive solution / existence / multiplicity

引用本文

导出引用
姚庆六. 奇异非线性边值问题的经典Agarwal-O'Regan方法. 数学学报, 2012, 55(5): 903-918 https://doi.org/10.12386/A2012sxxb0087
Qing Liu YAO. Classical Agarwal-O'Regan Method on Singular Nonlinear Boundary Value Problems. Acta Mathematica Sinica, Chinese Series, 2012, 55(5): 903-918 https://doi.org/10.12386/A2012sxxb0087

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基金

国家自然科学基金资助项目(11071109)
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