摘要
本文研究下面问题的正解其中Φp(s)=|s|p-2s,p>1．f在点x(i)=0,i=0,．．．,n-2可能是奇异的．证明建立在Leray-Schauder拓扑度和Vitali收敛定理的基础上．
This paper deals with the existence of positive solutions for the problem
{（Фp（x^（n-1）（t）））′＋f（t,x,…,x^（n-1）=0,0〈t〈1,
x^（i）（0）=0,0≤i≤n-3,
x^（n-2）（0）-B0（x^（n-1）（0））=0,x^（n-2）（1）＋B1（x^（x-1）（1））=0,
where Фp（s） = ｜s｜^p-2s, p 〉 1. f may be singular at x^（i） = 0, i = 0,...,n- 2. The proof is based on the Leray-Schauder degree and Vitali＇s convergence theorem.
基金
the National Natural Science Foundation of China (10371006)
the Foundation for PHD Specialities of Educational Department of China (20050007011).
关键词
高阶奇异微分方程
正解
Vitali收敛定理
singular higher-order differential equation
positive solution
Vitali＇s convergence theorem.
