# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.332996

Arkiv for Matematik, 41, (1), 105-114, 2001.7
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.
@inproceedings{sara2001infinitely,
title={Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain},