R^N上具有渐近线性项的奇异椭圆问题的研究(英文)  

Singular Elliptic Problems in R^N with Asymptotically Linear Nonlinearities

作　　者：彭超权[1] 刘颖[1] 王芳[1] 

机构地区：[1]中南民族大学数学与统计学院,湖北武汉430074

出　　处：《应用数学》2015年第2期303-309,共7页Mathematica Applicata

基　　金：Supported by the Special Found for Basic Scientific Research of Central College,SouthCentral University for Nationalities(CZY12013);the Postgraduate Innovation Foundation of SouthCentral University(2014sycxjj125)

摘　　要：本文通过变分方法,证明包含Hardy位势的奇异椭圆问题-Δu(x)-μ/|x|2u(x)=K(x)f(u),x ∈RN,x在u∈D1,2(RN)中至少有一个非平凡解,其中N≥3,0≤μ≤∶=((N-2)/2)2,f(t)是在R上的连续函数并且在无穷远处渐近线性.In this paper, via variational methods, we prove that the singular semilinear elliptic prob- lem involving hardy potential -Δu（x）-μ/｜x｜2u（x）=K（x）f（u）,x ∈RN,possess at least one nontrivial solution u∈D1,2（RN）,where N≥3,0≤μ≤∶=（（N-2）/2）2,f（t）is a continuous function on R and asymptotically linear as t → ∞.

关 键 词：非平凡解 HARDY位势 渐近线性 

分 类 号：O175.29[理学—数学]