## Arkiv för Matematik

- Ark. Mat.
- Volume 41, Number 1 (2003), 105-114.

### Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain

#### Abstract

We study a semilinear elliptic equation of the form
$ - \Delta u + u = f(x,u), u \in H_0^1 (\Omega ),$
where *f* is continuous, odd in *u* and satisfies some (subcritical) growth conditions. The domain Ω⊂R^{N} is supposed to be an unbounded domain (*N*≥3). We introduce a class of domains, called strongly asymptotically contractive, and show that for such domains Ω, the equation has infinitely many solutions.

#### Article information

**Source**

Ark. Mat., Volume 41, Number 1 (2003), 105-114.

**Dates**

Received: 17 July 2001

Revised: 19 May 2002

First available in Project Euclid: 31 January 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.afm/1485898794

**Digital Object Identifier**

doi:10.1007/BF02384570

**Mathematical Reviews number (MathSciNet)**

MR1971943

**Zentralblatt MATH identifier**

1088.35019

**Rights**

2003 © Institut Mittag-Leffler

#### Citation

Maad, Sara. Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain. Ark. Mat. 41 (2003), no. 1, 105--114. doi:10.1007/BF02384570. https://projecteuclid.org/euclid.afm/1485898794