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 gtech brush bar terms.For the superlinear (concave) term we do not employ the usual in such cases Ambrosetti-Rabinowitz condition.Using variational iphone 13 dallas methods together with truncation, perturbation and comparison techniques, we prove a bifurcation-type theorem describing the set of positive solutions as the parameter varies.