一类二阶奇异微分方程正解的存在唯一性

赵增勤

系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 325-333.

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系统科学与数学 ›› 2008, Vol. 28 ›› Issue (3) : 325-333. DOI: 10.12341/jssms10073
论文

一类二阶奇异微分方程正解的存在唯一性

    赵增勤
作者信息 +

Existence and Uniqueness of Positive Solutions for a Class of Second Order Singular Differential Equations

    ZHAO Zengqin
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摘要

利用上下解方法、不动点理论研究奇异微分方程u″+f(t,u)=0,t∈(0,1) 在边界条件 αu(0)−βu′(0)=0,γu(1)+δu′(1)=0下C[0,1]正解和C1[0,1]正解的存在性与唯一性. 其中非线性项f(t,u)关于u是减的,仅满足较弱的要求.

Abstract

The existence of positive solutions for a class of singular boundary value problems is investigated. Furthermore, the sufficient condition for the existence and uniqueness of positive solution of the system in C[0,1] and C1[0,1] is given respectively, by means of the method of lower and upper solution, and
the fixed point theorem.

关键词

奇异边值问题 / 正解 / 上下解 / 不动点定理.

Key words

Singular boundary value problem / positive solution / lower and upper solution / fixed point theorem.

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赵增勤. 一类二阶奇异微分方程正解的存在唯一性. 系统科学与数学, 2008, 28(3): 325-333. https://doi.org/10.12341/jssms10073
ZHAO Zengqin. Existence and Uniqueness of Positive Solutions for a Class of Second Order Singular Differential Equations. Journal of Systems Science and Mathematical Sciences, 2008, 28(3): 325-333 https://doi.org/10.12341/jssms10073
中图分类号： 34B15   
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