Geodesic
Multiple solutions for a \(q\)-Laplacian equation on an annulus
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we study the q-Laplacian equation

$ -\Delta_{q}u=\big||x|-2\big|^{a}u^{p-1},\quad 1|x|3 , $

where $\Delta_{q}u=\hbox{div}(|\nabla u|^{q-2} \nabla u)$ 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.
Classification : 35J40
Keywords: ground state, minimizer, nonradial function, q-Laplacian, Rayleigh quotient 
@article{EJDE_2012__2012__a11,
     author = {Tai,  Shijian and Wang,  Jiangtao},
     title = {Multiple solutions for a {\(q\)-Laplacian} equation on an annulus},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1241.35051},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a11/}
}
TY  - JOUR
AU  - Tai,  Shijian
AU  - Wang,  Jiangtao
TI  - Multiple solutions for a \(q\)-Laplacian equation on an annulus
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
UR  - http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a11/
LA  - en
ID  - EJDE_2012__2012__a11
ER  - 
%0 Journal Article
%A Tai,  Shijian
%A Wang,  Jiangtao
%T Multiple solutions for a \(q\)-Laplacian equation on an annulus
%J Electronic journal of differential equations
%D 2012
%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a11/
%G en
%F EJDE_2012__2012__a11
Tai,  Shijian; Wang,  Jiangtao. Multiple solutions for a \(q\)-Laplacian equation on an annulus. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a11/