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一类二阶非线性微分方程奇异边值问题唯一整体解的精确渐近行为

发表时间:2009-01-15  浏览量:1982  下载量:853
全部作者: 冯化冰,张志军
作者单位: 兰州大学数学与统计学院;烟台大学数学与信息科学学院
摘 要: 应用摄动方法和上下解方法,构造新的上下解,得到了一类半直线上二阶非线性微分方程奇异边值问题u″(t)=b(t)g(u(t)), u(t)>0, t>0, u(0)=∞, u(∞)=0唯一整体解ψ在无穷远处的精确渐近行为。这里,g∈C1[0,∞), g(0)=g′(0)=0, g在[0,∞)上单调递增,满足Keller-Osserman条件,g(s)/s在(0,∞)上单调递增;函数b∈C1(0, ∞), b在(0, ∞)上是正的单调递增函数。本文完善了此问题唯一整体解的性质。
关 键 词: 常微分方程;边值问题;唯一整体解;奇异性;渐近行为
Title: The exact variation speed of the unique entire solution to a singular boundary value problem for a class of second order nonlinear differential equations
Author: FENG Huabing, ZHANG Zhijun
Organization: School of Mathematics and Statistics, Lanzhou University; School of Mathematics and Informational Science, Yantai University
Abstract: By perturbation method and constructing new supersolution and subsolution, this paper derives the exact variation speed at infinity of the unique entire solution ψ to the following singular boundary value problem on the half-line u″(t)=b(t)g(u(t)), u(t)>0, t>0, u(0)=∞, u(∞)=0 where g∈C1[0,∞), g(0)=g′(0)=0, g is an increasing function in [0, ∞), satisfies Keller-Osserman condition, g(s)/s is an increasing function in (0, ∞); b∈C1(0,∞) is a positive increasing function in (0,∞). The paper completes the characteristics of the unique entire solution.
Key words: ordinary differential equation; boundary value problem; the unique entire solution; singularity; variation speed
发表期数: 2009年1月第1期
引用格式: 冯化冰,张志军. 一类二阶非线性微分方程奇异边值问题唯一整体解的精确渐近行为[J]. 中国科技论文在线精品论文,2009,2(1):80-84.
 
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