Geodesic
Multiple solutions for a $q$-Laplacian equation on an annulus
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Tai, Shijian and Wang, Jiangtao},
     title = {Multiple solutions for a $q${-Laplacian} equation on an annulus},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a11/}
}
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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/