Bifurcation analysis for nonhomogeneous Robin problems with competing nonlinearities

In this paper, we report on some recent results obtained in our joint paper Papageorgiou and Rădulescu (2015). We consider a Robin problem driven by a nonhomogeneous differential operator and with a reaction that exhibits competing effects of concave (that is, sublinear) and convex (that is, superlinear) nonlinearities. Without employing the Ambrosetti–Rabinowitz condition, we establish a bifurcation property of the positive solutions near the origin. The approach relies on variational methods and elliptic estimates.