%0 Journal Article
%T Multiple solutions for a q-Laplacian equation on an annulus
%A Shijian Tai
%A Jiangtao Wang
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X 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.
%K Ground state
%K minimizer
%K nonradial function
%K q-Laplacian
%K Rayleigh quotient
%U http://ejde.math.txstate.edu/Volumes/2012/16/abstr.html