Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator plus an indefinite potential and a reaction having the competing effects of concave and convex terms.For the ORIG HOT SAUCE superlinear (concave) term we do not employ the usual in such cases Ambrosetti-Rabinowitz condition.Using variational methods together with truncation, perturbation and Key Tags comparison techniques, we prove a bifurcation-type theorem describing the set of positive solutions as the parameter varies.