Infinitely many solutions of a symmetric semilinear elliptic equation on an unbounded domain
AbstractWe study a semilinear elliptic equation of the form
$$ - \Delta u + u = f(x,u), u \in H_0^1 (\Omega ),$$
 wheref is continuous, odd inu 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.