Anisotropic equations with indefinite potential and competing nonlinearities

We consider a nonlinear Dirichlet problem driven by a variable exponent p-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and a convex (superlinear) perturbation (the anisotropic concave-convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter lambda varies. Also, we prove the existence of minimal positive solutions. (C) 2020 Elsevier Ltd. All rights reserved.