抽象空间中二阶奇异脉冲微分方程边值问题的多个正解

Many Positive Solutions of Singular Boundary Value Problems for Second Functional Differential Equations with Impulse in Abstract Space

将一类二阶奇异脉冲微分方程的多个正解的存在性问题转化为积分算子的正不动点问题,根据Green函数的特点构造适当的锥F,在抽象空间中利用锥上不动点理论得出此边值问题的多个正解的存在性。

In this paper, we study the existence of positive solutions for a class of second order singular differential equations with impulse. The problem is transformed into the one for positive fixed point with integrate operator. By the character of Green function, we create a suitable cone F , then we conclude that the problem has positive solutions by the fixed point theory on the cone in abstract space.