二阶微分方程积分边值问题正解的存在性

Existence Positive Solutions of Boundary Value Problems for Second Order Differential Equations with Integral Conditions

研究一类满足Sturm-Liouville积分边值条件的二阶非线性微分方程的正解存在性.通过转化为等价的积分方程,利用锥上不动点定理及一些分析技巧,建立边值问题存在一个和多个正解的充分条件.该边值条件含有勒贝格-斯梯阶积分,所得的结果是新的.

We study the existence of positive solutions for Strum-Liouville boundary value problems of second-order non- linear functional differential equations. By converting problems into equivalent integra] equations, using fixed point theory in cones and some analysis techniques, we obtain some sufficient conditions which guarantee the existence of one and mub tiple positive solutions for the problem. The conditions of boundary value in this paper contain Stieltijes integral, and the obtained results are new.