RADIALLY SYMMETRIC SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING NONHOMOGENEOUS OPERATORS IN AN ORLICZ-SOBOLEV SPACE SETTING  

作　　者：Jae-Myoung KIM Yun-Ho KIM Jongrak LEE 

机构地区：[1]Department of Mathematics Education,Andong National University,Andong 36729,Republic of Korea [2]Department of Mathematics Education,Sangmyung University,Seoul 03016,Republic of Korea [3]Department of Mathematics,Jeju National University,Jeju 63243,Republic of Korea

出　　处：《Acta Mathematica Scientia》2020年第6期1679-1699,共21页数学物理学报（B辑英文版）

基　　金：the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2019R1F1A1057775);Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2018R1D1A1B07048620).

摘　　要：We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1<p<q<N,α<q,1<α≤p∗q′/p′with p∗=NpN−p,ϕ(t)behaves like t q/2 for small t and t p/2 for large t,and p′and q′are the conjugate exponents of p and q,respectively.We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem.Moreover,taking into account the dual fountain theorem,we show that the problem admits a sequence of small-energy,radially symmetric solutions.

关 键 词：radial solution quasilinear elliptic equations variational methods Orlicz-Sobolev spaces 

分 类 号：O175.25[理学—数学]