二阶时滞微分方程周期边值问题正解的三解定理

An Theorem About Triple Positive Solutions for PBVP of Second-Order Delay Differential Equations

利用Leggett-Williams不动点定理,研究了二阶时滞微分方程边值问题y″(t)+f(t,y(t-τ))=0,0<t<2π;y(t)=0,-τ≤t ≤0;y(0)=y(2π)正解的存在性.其中0<τ<π/2为一常数.我们先建立了该问题至少存在两个正解的充分条件.接着给出其至少存在三个正解的存在定理.

By means of the Leggett-Williams fixed-point theorem in cones. We study the existence of positive solutions for PBVP of second-order delay differential equation of the from {y＂（t）＋f（t,y（t-τ））=0,0〈t〈2π; y（t）=0,-τ≤t≤0; y（0）=y（2π） where r is a constant satisfied 0〈r〈π/2. We frist establish sufficient conditions which guarantee the existence of at least two positive solutions of this problem. Then we give the theorem of this problem which guarantee the existence of at least three positive solutions.