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Author: Valdinoci, Enrico × End date: 2019 × Start date: 2019 × DDC: 510 × Type: Report × Subject: Integrodifferential operators × Subject: fractional Laplacian ×

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    Asymptotically linear problems driven by fractional Laplacian operators
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Fiscella, Alessio; Servadei, Raffaella; Valdinoci, Enrico
    In this paper we study a non-local fractional Laplace equation, depending on a parameter, with asymptotically linear right-hand side. Our main result concerns the existence of weak solutions for this equation and it is obtained using variational and topological methods. We treat both the nonresonant case and the resonant one.
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    A nonlocal concave-convex problem with nonlocal mixed boundary data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Abdellaoui, Boumediene; Dieb, Abdelrazek; Valdinoci, Enrico
    The aim of this paper is to study a nonlocal equation with mixed Neumann and Dirichlet external conditions. We prove existence, nonexistence and multiplicity of positive energy solutions and analyze the interaction between the concave-convex nonlinearity and the Dirichlet-Neumann data.