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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2012-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/16/abstr.html |
| 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. |
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| ISSN: | 1072-6691 |