The Brezis–Oswald Result for Quasilinear Robin Problems
Copyright policy )The Brezis–Oswald Result for Quasilinear Robin Problems
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].
- National Technical University of Athens Greece
- Tuscia University Italy
- National Technical University Ecuador
- University of Bari Aldo Moro Italy
- University of Perugia Italy
Variational methods for second-order elliptic equations, Existence and Uniqueness of Positive Solutions, nonlinear nonhomogeneous differential operator, Robin Boundary Conditions, Nonlinear Nonhomogeneous Differential Operator, p-Laplacian, Nonlinear Green’s Identity, Nonlinear Picone’s Identity, Principal Eigenvalue, Nonlinear elliptic equations, Nonlinear Maximum Principle, Existence and Uniqueness of Positive Solutions; Nonlinear Maximum Principle; Nonlinear Nonhomogeneous Differential Operator; Nonlinear Picone's IdentityNonlinear Green's Identity; p-Laplacian; Principal Eigenvalue; Robin Boundary Conditions; Statistical and Nonlinear Physics; Mathematics (all)
Variational methods for second-order elliptic equations, Existence and Uniqueness of Positive Solutions, nonlinear nonhomogeneous differential operator, Robin Boundary Conditions, Nonlinear Nonhomogeneous Differential Operator, p-Laplacian, Nonlinear Green’s Identity, Nonlinear Picone’s Identity, Principal Eigenvalue, Nonlinear elliptic equations, Nonlinear Maximum Principle, Existence and Uniqueness of Positive Solutions; Nonlinear Maximum Principle; Nonlinear Nonhomogeneous Differential Operator; Nonlinear Picone's IdentityNonlinear Green's Identity; p-Laplacian; Principal Eigenvalue; Robin Boundary Conditions; Statistical and Nonlinear Physics; Mathematics (all)
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