奇异非线性边值问题的经典Agarwal-O'Regan方法  

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

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《数学学报（中文版）》2012年第5期903-918,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11071109)

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.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 prob- lems 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 sec- ond, 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 

分 类 号：O175.8[理学—数学]