二阶周期边值问题的多重正解

考虑如下周期边值问题:其中x~(1])(t)=p(t)x'(t).总假设p(t)>0,q(t)>0,且f(t,x)是0,1]×(0,+∞)→0,+∞)的连续函数,f在z=0可以有奇性.利用锥不动点定理以及格林函数的正性,给出周期边值问题单个和多个正解存在性证明的一种新方法.在实际中,定理的条件很容易验证.

Multiplicity of Positive-Solutions to Second Order Period Boundary Conditions

In this paper,we consider the following periodic boundary value problem: (?) where x(t) = p(t)x′(t).Throughout this paper we always assume that p(t)>0,q(t)>0, and the function f(t,x) satisfies f:0,1]×(0,+∞)→0,+∞) is continuous,f may be singular at x=0. In this paper we shall present a new existence theory for single and multiple positive periodic solutions for periodic boundary value problems by applying a well-known fixed point theorem in cones(see Theorem 2.3).The conditions in our main theorems can easily be checked in practice.