一类具Hardy-Sobolev临界增长拟线性椭圆方程的径向解  

Radial solutions for a quasilinear elliptic equation with a crittical Hardy-Sobolev growth

作　　者：占兰兰 陈南博 刘期怀[1] ZHAN Lanlan;CHEN Nanbo;LIU Qihuai(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期93-97,共5页Journal of Guilin University of Electronic Technology

基　　金：广西科技基地与人才专项(桂科AD21075019);桂林市科技项目(20210218-3)。

摘　　要：考虑一类具有临界Hardy-Sobolev指数的p-Laplace拟线性椭圆方程及其扰动问题的径向解的存在性,通过Lions引理和非线性泛函理论知识建立Sobolev空间到加权Lebesgue空间的紧嵌入定理,并利用极小化方法,得到了上述问题在全空间和有界区域上的径向解的存在性。In this paper,the existence of radial solutions of p-Laplace quasilinear elliptic equations with critical Hardy-Sobolev exponents and perturbation problems are considered.A compact embedding theorem from Sobolev space to weighted Lebesgue space is established by means of Lions lemma and nonlinear functional theory.The existence of radial solutions in the whole space and bounded region is obtained.

关 键 词：临界Hardy-Sobolev指数 加权Lebesgue空间 紧嵌入 极小化方法 

分 类 号：O175.25[理学—数学]