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.