具有Strum-Liouville边界条件的四阶奇异超线性微分方程正解的存在性和不存在性

Existence And Nonexistence of Positive Solutions for Fourth order Singular Superlinear Differential Equations with Strum-Liouville Boundary Conditions

本文给出Strum-Liouville边界条件下的一类四阶奇异超线性微分方程其C^2[0,1]正解存在的充分必要条件和C^3[0,1]正解存在的充分条件和必要条件.结果可用于判断给定的边值同题其正解的存在性与不存在性.

This paper investigates a class of fourth order singular superlinear differential equations with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C^2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C^3 [0, 1] positive solutions. The results are used to judge existence and nonexistence of positive solutions for given boundary value problems.