奇异二阶非线性两点边值问题正解的研究

Study of positive solutions of singular second order nonlinear two-point boundary value problem

对于带奇异的二阶非线性两点边值问题的正解存在性的研究,由于问题的奇异性,使得很多适用于研究非奇异问题的工具变得不再适用;寻求适用于研究奇异问题的工具就变得重要。这一问题已有不少研究,其中运用了打靶法和上下解法。除了在研究方法上运用锥上的不动点定理得到了一组两个正解存在性的充分条件。对于非线性项的推广也显得很重要。以往的大多数研究集中在纯粹亚线性或者纯粹超线性情形,本文研究了亚线性和超线性混合的情况。

The study of the existence of positive solutions of singular nonlinear two-point boundary value problems, because of the singularity of the problem, many technique that valid to the nonlinear case are not valid again. To find a technique that valid to the study of singular problem is very important. We use a fixed point theorem on cones to find a sufficient condition of the existence of two positive solutions. Be-sides, to wide the nonlinearity is very important. We here consider lower-linear and supper-linear cases.