Abstract

We obtain, for N ? 4, the existence of a positive solution as well as a nonradial solution, which changes the sign of the equation-?u + V(z)u = f(z,u)in ?Nu ? H1(?N), where the function f is a superlinear nonlinearity and the function V is a potential that is bounded below by a positive constant. As a consequence, we complete for the case V(z) ? 1 and f(z,u) ? f(u) the well-known work of Bartsh and Willen (J. Funct. Anal. 117 (1993) 261.) because there it does not consider the case N = 5. © 2004 Elsevier Ltd. All rights reserved.