| 环域上一类拟线性椭圆型方程的正径向解的存在性 |
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| 引用本文： | 张辉,郭宗明.环域上一类拟线性椭圆型方程的正径向解的存在性[J].高校应用数学学报(英文版),1999,14(3):313-320. |
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| 作者姓名： | 张辉 郭宗明 |
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| 作者单位： | [1]Dept.ofMath.,HenanNormalUniv.,Xinxiang453002. [2]InstituteofSystemsScience,AcademiaSinica,Beijing100080. |
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| 基金项目： | 教育部青年基金，Committee of Science and Technology of Henan Province |
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| 摘 要： | The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^ f‘ (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge positive radial solution on all annuli. If f(0)≤0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide.
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| 关 键 词： | 存在性 正径向法 椭圆方程 环型区域 |
| 收稿时间： | 15 May 1998 |
Existence of positive radial solutions for some quasilinear elliptic equations in annular domains |
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| Hui Zhang,Zongming Guo.Existence of positive radial solutions for some quasilinear elliptic equations in annular domains[J].Applied Mathematics A Journal of Chinese Universities,1999,14(3):313-320. |
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| Authors: | Hui Zhang Zongming Guo |
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| Institution: | (1) Dept. of Math., Henan Normal Univ., 453002 Xinxiang;(2) Institute of Systems Science, Academia Sinica, 100080 Beijing |
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| Abstract: | The existence of positive radial solutions of the equation-div(|Du|
p−2
Du)=f(u) is studied in annular domains in R
n, n≥2. It is proved that if f(0)≥0, f is somewhere negative in (0, ∞), lim
u→0+f′(u)=0 and lim
u→∞(f(u)/u
p−1)=∞, then there is a large positive radial solution on all annuli. If f(0)<0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide.
Supported by the Youth Foundations of National Education Committee of China and the Committee of Science and Technology of
Henan Province. |
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| Keywords: | Quasilinear elliptic equations large solutions positive radial solutions annular domains |
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