a1 Department of Mathematics, Hellenic Naval Academy, Piraeus 18539, Greece (email@example.com)
a2 Department of Mathematics, National University of Ireland, Galway, Ireland (firstname.lastname@example.org)
a3 Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece (email@example.com)
We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a reaction term which exhibits a (p – 1)-superlinear growth near ±∞ but need not satisfy the Ambrosetti-Rabinowitz condition. Combining critical point theory with Morse theory we prove an existence theorem. Then, using variational methods together with truncation techniques, we prove a multiplicity theorem establishing the existence of at least five non-trivial solutions, with precise sign information for all of them (two positive solutions, two negative solutions and a nodal (sign changing) solution).
(Received September 04 2011)
2010 Mathematics subject classification