On superlinear problems without the Ambrosetti and Rabinowitz condition

Existence and multiplicity results are obtained for superlinear pp-Laplacian equations without the Ambrosetti and Rabinowitz condition. To overcome the difficulty that the Palais–Smale sequences of the Euler–Lagrange functional may be unbounded, we consider the Cerami sequences. Our results extend the recent results of Miyagaki and Souto [O. Miyagaki, M. Souto, Superlinear problems without Ambrosetti and Rabinowitz growth condition, J. Differential Equations 245 (2008) 3628–3638].