Some uniqueness results in quasilinear subhomogeneous problems

Abstract

We establish uniqueness results for quasilinear elliptic problems through the criterion recently provided in [6]. We apply it to generalized p-Laplacian subhomogeneous problems that may admit multiple nontrivial nonnegative solutions. Based on a generalized hidden convexity result, we show that uniqueness holds among strongly positive solutions and nonnegative global minimizers. Problems involving nonhomogeneous operators as the socalled (p, r)-Laplacian are also treated.