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
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⊂RN 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.
Ark. Mat., Volume 41, Number 1 (2003), 105-114.
Received: 17 July 2001
Revised: 19 May 2002
First available in Project Euclid: 31 January 2017
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2003 © Institut Mittag-Leffler
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