Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

Abstract

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 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 describing the set of positive solutions as the parameter varies.

Keywords

• Nonhomogeneous differential operator
• positive solution
• local minimizer
• nonlinear maximum principle
• mountain pass theorem
• bifurcation