奇异半正Sturm-Liouville方程边值问题的正解

Positive Solutions to the Singular Semi-positone Sturm-Liouville Boundary Value Problem

本文研究超线性Sturm-Liouville方程的边值问题,其中非线性项可变号且在端点处具有奇异性。利用锥上的不动点指数定理和平移变换的方法,我们得到奇异半正边值问题至少存在一个更广泛意义的正解及正解的性质。本文考虑的是一般形式的方程和边值条件,改进了之前的结果。

In this paper, we investigate boundary value problems of super-linear Sturm-Liouville differential equations when the nonlinearity may change sign and may be singular at the endpoints. Existence of at least one positive solutions in a broader sense and the property of the positive solutions of singular semi-positone boundary value problems are obtained by using the fixed point index theory on a cone and the method of transformation. We consider the general form of differential equations and boundary conditions, so the obtained results improve the existing conclusions.