Abstract

In this paper we study the existence of least energy solutions to subcritical semilinear elliptic equations of the form ?u - u + f(u) = 0 in ?, u > 0 in ?, u = 0 on ??, u(z) ? 0 as |z| ? ?, z ? ?, where ? is an unbounded domain in RN and f is a C1 function, with appropriate superlinear growth. We state general conditions on the domain ? so that the associated functional has a nontrivial critical point, thus yielding a solution to the equation. Asymptotic results for domains stretched in one direction are also provided.