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Asymptotically linear problems driven by fractional Laplacian operators
Author(s) -
Fiscella Alessio,
Servadei Raffaella,
Valdinoci Enrico
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3438
Subject(s) - mathematics , fractional laplacian , laplace operator , laplace transform , stability theory , mathematical analysis , nonlinear system , physics , quantum mechanics
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 non‐resonant case and the resonant one. Copyright © 2015 John Wiley & Sons, Ltd.