一类奇异Sturm-Liouville边值问题正解存在的充分必要条件

A Necessary and Sufficient Condition for Existence of Positive Solutions to a Class of Singular Sturm-Liouville Boundary Value Problems

研究了奇异二阶微分方程u″(t)+f(t,u(t))=0,t∈(0,1)适合Sturm-Liouville边值条件αu(0)-βu′(0)=0,γu(1)+δu′(1)=0,下的C1[0,1]正解的存在性,利用锥上的不动点定理得到了奇异边值问题C1[0,1]正解存在的一个充分必要条件.

This paper studies the existence of positive solutions for singular second-order differential equations subject to Sturm-Liouville boundary value conditions αu （0） -- βu′ （0） = 0, γu （1） ＋ δu′ （1） = 0, A necessary and sufficient condition for the existence of C′ [0,1] positive solutions of singular boundary value problems is obtained by the means of fixed point theorems on cones.