三阶微分方程组边值问题常号解的存在性

孙忠民;赵增勤

系统科学与数学 ›› 2007, Vol. 27 ›› Issue (6) : 811-819.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2007, Vol. 27 ›› Issue (6) : 811-819. DOI: 10.12341/jssms10021
论文

三阶微分方程组边值问题常号解的存在性

    孙忠民(1), 赵增勤(2)
作者信息 +

The Existence of Constant-Sign Solutions of Bvps for Third OrderDifferential Systems

    Sun Zhongmin (1), Zhao Zengqin(2)
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文章历史 +

摘要

利用Krasnoselskii不动点定理,结合Leray-Schauder度,研究下列三阶微分方程组边值问题
{ui‴(t)=fi(t,u1(t),u2(t),u3(t)),t∈[0,1],ui′(0)=ui″(0)=ui(1)=0,i=1,2,3.
在某些条件下,常号解的存在性和多解性.

Abstract

Consider the following third-order system of two-point boundary value problems:
{ui‴(t)=fi(t,u1(t),u2(t),u3(t)),t∈[0,1],ui′(0)=ui″(0)=ui(1)=0,i=1,2,3.Using a nonlinear alternative of Leray-Schauder type and
Krasnoselskii's fixed point theorem, we establish the existence of one or more constant-sign solutions for the system.

关键词

三阶微分方程组 / 边值问题 / 常号解.

Key words

Third-order differential systems / constant-sign solutions / boundary value problems.

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孙忠民 , 赵增勤. 三阶微分方程组边值问题常号解的存在性. 系统科学与数学, 2007, 27(6): 811-819. https://doi.org/10.12341/jssms10021
Sun Zhongmin , Zhao Zengqin. The Existence of Constant-Sign Solutions of Bvps for Third OrderDifferential Systems. Journal of Systems Science and Mathematical Sciences, 2007, 27(6): 811-819 https://doi.org/10.12341/jssms10021
中图分类号： 34B15   
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