p-Laplacian problems with nonlinearities interacting with the spectrum

The aim of this paper is investigating the existence and the multiplicity of solutions of a quasilinear elliptic problem of p-Laplacian type on an open bounded domain of $R^N$ with smooth boundary and the nonlinearity g behaves as $u^{p-1}$ at infinity. The main tools of the proof are some abstract critical point theorems, but extended to Banach spaces, and two sequences of quasi-eigenvalues for the p-Laplacian operator. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdA