LEAST ENERGY SOLUTIONS FOR ELLIPTIC-EQUATIONS IN UNBOUNDED-DOMAINS

In this paper we study the existence of least energy solutions to subc ritical semilinear elliptic equations of the form Delta u-u + f(u) = 0 in Omega, u > 0 in Omega, u = 0 on partial derivative Omega, u(z)-->0 as \z\-->infinity, z epsilon Omega, where Omega is an unbounded domai n in R(N) and fis a C-1 function, with appropriate superlinear growth. We state general conditions on the domain Omega so that the associate d functional has a nontrivial critical point, thus yielding a solution to the equation. Asymptotic results for domains stretched in one dire ction are also provided.