From the introduction: We prove the existence of multiple solutions for the Neumann boundary value problem
where is a smooth bounded domain of , , , , in . We always assume that as . In the present paper, for general domains , with the help of the concentration-compactness argument, we first obtain the “ground state solution” and then combine it with some ideas of G. Cerami, S. Solimini and M. Struwe [J. Funct. Anal. 69, 289-306 (1986; Zbl 0614.35035)] to prove the existence of another solution which changes sign.