Symmetric and nonsymmetric solutions for an elliptic equation on RN Original Research Article

We obtain, for N⩾4, the existence of a positive solution as well as a nonradial solution, which changes the sign of the equation View the MathML source 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.