Nonlinear, Nonhomogeneous Periodic Problems with no Growth Control on the Reaction
Leszek Gasiński, Nikolaos S. Papageorgiou · Journal of Dynamical and Control Systems · 2014
We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator, which includes as a particular case the scalar p -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.