二阶常微分方程周期边值问题的三解定理  

A THEOREM OF THREE SOLUTIONS FOR PERIODIC BOUNDARY VALUE PROBLEMS OF SECOND ORDER DIFFERENTIAL EQUATION

作　　者：张福保[1] 

机构地区：[1]南京大学数学系

出　　处：《系统科学与数学》2000年第3期257-263,共7页Journal of Systems Science and Mathematical Sciences

摘　　要：在有两对严格上下解的假定下，通过一些构造和连合度的计算，证明了一般的非线性二阶常微分方程周期边值问题至少有三个不同的解的结果．作为应用，讨论了Li6nard方程的多解问题．Under the condition that there exist two pairs of strictly upper and lowersolutions, a three-solution theorem for periodic boundary value problem of a generalized non-linear second order ordinary differential equation is obtained by means of the coincidence degreemethod. As an application, the multiple solutions of Lienard equation are obtained.

关 键 词：周期边值问题 三解定理 常微分方程 非线性 

分 类 号：O175[理学—数学]