单位球上含梯度项的椭圆边值问题的正径向解  

Positive radial solutions for the elliptic boundary value problem with gradient terms on the unit ball

作　　者：唐颖 李永祥 TANG Ying;LI Yong-Xiang(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2021年第6期22-26,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(12061062;11661071);校级科研基金(2020KYZZ001110)。

摘　　要：本文考虑了单位球Ω={x∈R^(N):|x|<1}上含梯度项的椭圆边值问题{-Δu=f(|x|,u,|■u|),x∈Ω,u|δΩ=0正径向解的存在性,其中N≥2,f:[0,1]×R^(+)×R^(+)→R^(+)连续.在f(r,ξ,η)满足一些不等式的条件下,本文应用Leray-Schauder不动点定理获得了问题正径向解的存在性.We consider the existence of positive radial solutions of the elliptic boundary value problem with gradient term{-Δu=f(|x|,u,||■u|),x∈Ω,u|δΩ=0whereΩ={x∈R^(N):|x|<1},N≥2,f:[0,1]×R^(+)×R^(+)→R^(+)is continuous.Under the condition that f(r,ξ,η)satisfies certain inequalities,the existence of positive radial solutions is obtained by using the Leray-Schauder fixed point theorem.

关 键 词：单位球上的椭圆边值问题 正径向解 Nagumo型增长条件 LERAY-SCHAUDER不动点定理 

分 类 号：O175.25[理学—数学]