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

We study a semilinear elliptic equation of the form wheref is continuous, odd inu 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.