Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

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