## Topological Methods in Nonlinear Analysis

### Partially symmetric solutions of the generalized Hénon equation in symmetric domains

Ryuji Kajikiya

#### Abstract

We study the generalized Hénon equation in a symmetric domain $\Omega$. Let $H$ and $G$ be closed subgroups of the orthogonal group such that $H \varsubsetneq G$ and $\Omega$ is $G$ invariant. Then we show the existence of a positive solution which is $H$ invariant but $G$ non-invariant under suitable assumptions of $H,G$ and the coefficient function of the equation.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 191-221.

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343891

Digital Object Identifier
doi:10.12775/TMNA.2015.043

Mathematical Reviews number (MathSciNet)
MR3443684

Zentralblatt MATH identifier
06712684

#### Citation

Kajikiya, Ryuji. Partially symmetric solutions of the generalized Hénon equation in symmetric domains. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 191--221. doi:10.12775/TMNA.2015.043. https://projecteuclid.org/euclid.tmna/1459343891

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