| 含梯度项椭圆边值问题正径向解的存在性 |
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| 引用本文： | 伏彤彤,李永祥. 含梯度项椭圆边值问题正径向解的存在性[J]. 吉林大学学报(理学版), 2021, 59(3): 435-443. DOI: 10.13413/j.cnki.jdxblxb.2020293 |
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| 作者姓名： | 伏彤彤 李永祥 |
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| 作者单位： | 西北师范大学 数学与统计学院, 兰州 730070 |
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| 摘 要： | 用上下解方法讨论球外部区域Ω={x∈?N:∣x∣>R0}上含梯度项的椭圆边值问题:{-Δu=K(∣x∣)f(∣x∣,u,∣?u∣),x∈Ω,αu+β?u/?n∣?Ω=0,lim∣x∣→∞u(x)=0正径向解的存在性与唯一性,其中N≥3,R0>0,K:[R0,∞)→?+和f:[R0,∞)×?×?+→?连续.在系数函数K(...
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| 关 键 词： | 椭圆边值问题 正径向解 外部区域 Nagumo条件 上解 下解 |
| 收稿时间： | 2020-09-28 |
Existence of Positive Radial Solutions for Elliptic Boundary Value Problems with Gradient Terms |
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| FU Tongtong,LI Yongxiang. Existence of Positive Radial Solutions for Elliptic Boundary Value Problems with Gradient Terms[J]. Journal of Jilin University: Sci Ed, 2021, 59(3): 435-443. DOI: 10.13413/j.cnki.jdxblxb.2020293 |
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| Authors: | FU Tongtong LI Yongxiang |
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| Affiliation: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China |
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| Abstract: | Using the method of upper and lower solutions, we discuss the existence and uniqueness of positive radial solutions for elliptic boundary value problems with gradient term:When the coefficient function K(r)=O(1/r2(N-1))(r→+∞), under the condition that the nonlinear term f(r,u,η） satisfies some appropriate inequality conditions and Nagumo condition on η, we prove the existence and uniqueness of the positive radial solution of the problem. |
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| Keywords: | elliptic boundary value problem positive radial solution exterior domain Nagumo condition upper solution lower solution |
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