非线性电报方程组的3个双周期正解问题  

Triple Positive Doubly Periodic Solutions of a Nonlinear Telegraph System

作　　者：王方磊[1] 安玉坤[1] 

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《应用数学和力学》2009年第1期83-89,共7页Applied Mathematics and Mechanics

摘　　要：主要考虑了带有双周期边值条件的耦合的非线性电报方程组的至少有3个双周期正解的存在性.首先利用线性电报方程的Green函数和极值原理,将非线性电报方程组解的存在性转化为算子的不动点.其次赋予非线性项一定的增长条件,然后利用有序Banach空间锥上的Leggett-Williams不动点定理来证明算子在锥中至少存在3个不动点,即非线性电报方程组至少3个非负双周期解的存在性.There exist at least three positive doubly periodic solutions of a coupled nonlinear telegraph system with doubly periodic boundary conditions. First, using the Green function and maximum principle, the existence of solutions of nonlinear telegraph system was equivalent to the existence of fixed points of an operator. Finally, imposing growth conditions on the nonlinearities, the existence of at least three fixed points in cone was obtained by using the Leggett-Williams fixed point theorem to cones in ordered Banach spaces, namely, there exist at least three positive doubly periodic solutions of the nonlinear telegraph system.

关 键 词：电报方程组 双周期解 锥 不动点定理 

分 类 号：O175.15[理学—数学] O177.91[理学—基础数学]