摘要
This article proves existence results for singular problem ( - 1)n-px(n)(t) = f(t,x(t),…,x(n-1)(t)), for 0 < t < l,x(i)(0) = 0,i = 1,2.…,p - l,x(i)(1) = 0,i = p,p + 1,…, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f(t,x0,x1,…,xn-1) are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali's convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.
This article proves existence results for singular problem （-1）^n-px^（n）（t） = f（t,x（t）,……,x^（n-1）（t））, for 0 〈 t 〈 1,x^（i）（0） = 0, i = 1,2,……,p- 1,x^（i）（1） = 0, i = p,p ＋ 1,……, n - 1. Here the positive Carathedory function f may be singular at the zero value of all its phase variables. The interesting point is that the degrees of some variables in the nonlinear term f（t, xo,x1,……,xn-1） are allowable to be greater than 1. Proofs are based on the Leray-Schauder degree theory and Vitali＇s convergence theorem. The emphasis in this article is that f depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.
出处
《数学物理学报（A辑）》
CSCD
北大核心
2006年第B12期1064-1076,共13页
Acta Mathematica Scientia
基金
Supported by National Natural Sciences Foundation of China(10371006)Foundation for PhD Specialities of Educational Department of China(20050007011).
关键词
高阶微分方程
边值问题
集中收敛定理
规则化
Right focal
Singular higher-order differential equation
Regularization
Vitali＇s convergence theorem
作者简介
E-mail： tianyu2992@163.com
