title: Nonlinear, Nonhomogeneous Periodic Problems with no Growth Control on the Reaction.
abstract: We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator, which includes as a particular case the scalarp-Laplacian. We assume that the reaction is a Carathéodory function which admits time-dependent zeros of constant sign. No growth control near ±∞ is imposed on the reaction. Using variational methods coupled with suitable truncation and comparison techniques, we prove two multiplicity theorems providing sign information for all the solutions.
authors.affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland.
authors.forename: Leszek
authors.initials: L
authors.lastname: Gasiński
authors.affiliation: Department of Mathematics, National Technical University, Zografou Campus, 157 80 Athens, Greece.
authors.forename: Nikolaos S
authors.initials: NS
authors.lastname: Papageorgiou
keywords: Constant sign solutions; Mountain pass theorem; Nodal solutions; Nonhomogeneous differential operator; Nonlinear strong maximum principle; Second deformation theorem