Multiplicity of Solutions for Doubly Resonant Neumann Problems

In this paper,we examine semilinear Neumann problems which at +/-infinity are resonant with respect to two successive eigenvalues (double resonance situation). Using variational methods based on the critical point theory together with Morse theory, we prove two multiplicity results. In the first we obtain two nontrivial solutions and in the second three, two of which have constant sign (one positive, the other negative).