We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting.

Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions / Pinamonti, Andrea; Vecchi, Eugenio; Mugnai, Dimitri. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1432-0835. - 2020/59:2(2020), pp. 4301-4325. [10.1007/s00526-020-1708-8]

Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions

Andrea Pinamonti;
2020-01-01

Abstract

We consider a boundary value problem driven by the p-fractional Laplacian with nonlocal Robin boundary conditions and we provide necessary and sufficient conditions which ensure the existence of a unique positive (weak) solution. The results proved in this paper can be considered a first step towards a complete generalization of the classical result by Brezis and Oswald (Nonlinear Anal 10:55–64, 1986) to the nonlocal setting.
2020
2
Pinamonti, Andrea; Vecchi, Eugenio; Mugnai, Dimitri
Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions / Pinamonti, Andrea; Vecchi, Eugenio; Mugnai, Dimitri. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1432-0835. - 2020/59:2(2020), pp. 4301-4325. [10.1007/s00526-020-1708-8]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/266890
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