Uniqueness of the critical point for solutions of some \(p\)-Laplace equations in the plane (Q6060935)

Summary: We prove that quasi-concave positive solutions to a class of quasi-linear elliptic equations driven by the \(p\)-Laplacian in convex bounded domains of the plane have only one critical point. As a consequence, we obtain \textit{strict concavity} results for suitable transformations of these solutions.