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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Bibliographic Details
Main Authors: Shijian Tai, Jiangtao Wang
Format: Article
Language:English
Published: Texas State University 2012-01-01
Series:Electronic Journal of Differential Equations
Subjects:
Online Access:http://ejde.math.txstate.edu/Volumes/2012/16/abstr.html
Description
Summary: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.
ISSN:1072-6691