不动点指数理论下非线性Neumann型边值问题正解的存在性(英文)  

Existence of the Positive Solutions to the Nonlinear Boundary Value Problem of Neumann Type via Fixed-point Index Theory

作　　者：周文学[1,2] 彭济根[2] 

机构地区：[1]兰州交通大学数学系,兰州730070 [2]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2011年第5期589-597,共9页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(10901075);the Key Project of Education Ministry of China(210226)

摘　　要：应用Green函数可以将微分方程边值问题转化为等价的积分方程.近来此方法被应用于讨论微分方程边值问题正解的存在性.本文讨论非线性二阶Neumann边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项在无穷远处有增长条件,利用锥上的不动点指数理论证明正解的存在性和非存在性.By the means of the Green’s function, the boundary value problem of differential equation can be reduced to the equivalent integral equation. Recently, this method is used successfully to discuss the existence of the positive solutions to the boundary value problem of nonlinear differential equation. This article investigates the nonlinear Neumann boundary value problem. Applying growth conditions on the nonlinear terms, we obtain the existence and nonexistence results for the positive solutions by the fixed point index theory in cones.

关 键 词：NEUMANN边值问题 正解 锥 不动点指数理论 

分 类 号：O175.8[理学—数学]