变系数二阶Neumann边值问题正解的存在性

Existence of positive solutions for second-order Neumann boundary value problem with a variable coefficient

应用锥上的不动点定理,研究变系数二阶Neumann边值问题{x″(t)+m2(t)x(t)=f(t)g(t,x(t)),t∈(0,1),x′(0)=0,x′(1)=0正解的存在性,其中m∈C([0,1],(0,+∞)),f,g可以在t=0,1或x=0处奇异.给出了此类问题有一个正解存在的充分条件,所获主要结果推广和改进了一些已有的结果.

In this paper, the existence of positive solutions for the second-order Neumann boundary value problem with a variable coefficient {x＂（t）＋m2（t）x（t）=f（t）g（t,x（t））,t∈（0,1）x＇（0）=0,x＇（1）=0 is studied, where m ∈ C（[0, 1], （0,＋∞））, f, g may be singular at t = 0, 1 or x =0. By using the fixed point theorem, the sufficient conditions for the existence of positive solutions of the above mentioned problem are obtained. The theorems obtained improve and extend previous known results.