变分法研究半直线上二阶微分方程由边值条件产生的多个解(英文)  

Multiple Solutions for Second-order Differential Equation Generated from a Boundary Condition on the Half-line Via Variational Methods

作　　者：李培峦[1,2] 袁合才[3] 徐昌进[4] 

机构地区：[1]湖南师范大学数学科学与计算技术学院,湖南长沙410081 [2]河南科技大学数学与统计学院,河南洛阳471003 [3]华北水利水电学院数信学院,河南郑州450045 [4]贵州省经济系统仿真重点实验室,贵州财经大学,贵州贵阳550004

出　　处：《应用数学》2012年第4期847-853,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (10871206 , 11001274 , 11101126);the Chinese Postdoctoral Science Foundation (20110491249)

摘　　要：本文讨论半直线上的一类具有非线性边值条件的二阶微分方程.利用变分法和B.Ricceri的三临界点定理得到该方程的多个正解.同时建立该方程由边值条件产生的两个解存在的充分条件.最后给出一个例子来阐释本文的结果.In this paper, we investigate a second-order differential equation with nonlinear boundary conditions on the half-line. Multiplicity of solutions for the second-order differential equations on the half-line are considered by variational methods and a three-critical-points theorem by B. Ricceri. We also establish sufficient conditions under which such a system possesses two solutions generated from a boundary condition. To illustrate the main results,an example is given.

关 键 词：多解性 变分法 半直线 由边值条件产生的解 

分 类 号：O175[理学—数学]