Electron. J. Diff. Eqns., Vol. 2009(2009), No. 40, pp. 1-5.

A note on nodal non-radially symmetric solutions to Emden-Fowler equations

Miguel Ramos, Wenming Zou

Abstract:
We prove the existence of an unbounded sequence of sign-changing and non-radially symmetric solutions to the problem $-\Delta u = |u|^{p-1}u$ in $\Omega$, $u = 0$ on $\partial\Omega$, $u(gx)= u(x$), $ x\in \Omega$, $g\in G$, where $\Omega$ is an annulus of $\mathbb{R}^N$ ($N\geq 3$), $1<p< (N+2)/(N-2)$ and $G$ is a non-transitive closed subgroup of the orthogonal group $O(N)$.

Submitted February 19, 2009. Published March 19, 2009.
Math Subject Classifications: 35J20, 35J25, 35B99.
Key Words: Emden-Fowler equation; nodal solutions; symmetric solutions; variational methods.

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Miguel Ramos
Universidade de Lisboa, CMAF-Faculty of Science
Av. Prof. Gama Pinto, 2, 1649-003-Lisboa, Portugal
email: mramos@ptmat.fc.ul.pt
Wenming Zou
Department of Mathematical Sciences, Tsinghua University
Beijing 100084, China
email: wzou@math.tsinghua.edu.cn

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