Multiple solutions for a q-Laplacian equation on an annulus
In this article, we study the q-Laplacian equation $$ -Delta_{q}u=ig||x|-2ig|^{a}u^{p-1},quad 1<|x|<3 , $$ where $Delta_{q}u=hbox{div}(|abla u|^{q-2} abla u)$ and $q>1$. We prove that the problem has two solutions when $a$ is large, and has two additional solutions when $p$ is...
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Texas State University
2012-01-01
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doaj-b2679315e01d4e14b22d3359033ebfd42020-11-24T23:29:30ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-01-01201216,115Multiple solutions for a q-Laplacian equation on an annulusShijian TaiJiangtao WangIn this article, we study the q-Laplacian equation $$ -Delta_{q}u=ig||x|-2ig|^{a}u^{p-1},quad 1<|x|<3 , $$ where $Delta_{q}u=hbox{div}(|abla u|^{q-2} abla u)$ and $q>1$. We prove that the problem has two solutions when $a$ is large, and has two additional solutions when $p$ is close to the critical Sobolev exponent $q^{*}=frac{Nq}{N-q}$. A symmetry-breaking phenomenon appears which shows that the least-energy solution cannot be radial function. http://ejde.math.txstate.edu/Volumes/2012/16/abstr.htmlGround stateminimizernonradial functionq-LaplacianRayleigh quotient |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shijian Tai Jiangtao Wang |
spellingShingle |
Shijian Tai Jiangtao Wang Multiple solutions for a q-Laplacian equation on an annulus Electronic Journal of Differential Equations Ground state minimizer nonradial function q-Laplacian Rayleigh quotient |
author_facet |
Shijian Tai Jiangtao Wang |
author_sort |
Shijian Tai |
title |
Multiple solutions for a q-Laplacian equation on an annulus |
title_short |
Multiple solutions for a q-Laplacian equation on an annulus |
title_full |
Multiple solutions for a q-Laplacian equation on an annulus |
title_fullStr |
Multiple solutions for a q-Laplacian equation on an annulus |
title_full_unstemmed |
Multiple solutions for a q-Laplacian equation on an annulus |
title_sort |
multiple solutions for a q-laplacian equation on an annulus |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2012-01-01 |
description |
In this article, we study the q-Laplacian equation $$ -Delta_{q}u=ig||x|-2ig|^{a}u^{p-1},quad 1<|x|<3 , $$ where $Delta_{q}u=hbox{div}(|abla u|^{q-2} abla u)$ and $q>1$. We prove that the problem has two solutions when $a$ is large, and has two additional solutions when $p$ is close to the critical Sobolev exponent $q^{*}=frac{Nq}{N-q}$. A symmetry-breaking phenomenon appears which shows that the least-energy solution cannot be radial function. |
topic |
Ground state minimizer nonradial function q-Laplacian Rayleigh quotient |
url |
http://ejde.math.txstate.edu/Volumes/2012/16/abstr.html |
work_keys_str_mv |
AT shijiantai multiplesolutionsforaqlaplacianequationonanannulus AT jiangtaowang multiplesolutionsforaqlaplacianequationonanannulus |
_version_ |
1725545281399816192 |