Existence and multiplicity for a resonance problem for the p-Laplacian on bounded domains in RN

The existence of at least two solutions for a resonance problem involving the p-Laplacian is shown for the case of bounded domains in RN. This work constitutes an extension of a previous result of Landesman, Robinson and Rumbos for the case p=2 [E. Landesman, S. Robinson, A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Analysis TMA 24 (7) (1995) 1049-1059].