The Brezis–Oswald Result for Quasilinear Robin Problems

Abstract

Abstract In this paper we consider a nonlinear elliptic problem driven by a nonhomogeneous differential operator with Robin boundary conditions. We produce conditions on the reaction term near 0 + ${0^{+}}$ and near + ∞ ${+\infty}$ , which imply the existence and uniqueness of a positive solution. In the particular case of equations driven by the p-Laplacian, we show that these conditions are also necessary, extending in this way the semilinear Dirichlet work of Brezis and Oswald [5].