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 $0^+$ and near $+ ∞$, 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].
The Brezis-Oswald Result for Quasilinear Robin Problems
FRAGNELLI, Genni;
2016-01-01
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 $0^+$ and near $+ ∞$, 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].File in questo prodotto:
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