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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 13, Issue 1


Volume 13 (2015)

Semilinear problems for the fractional laplacian with a singular nonlinearity

Begoña Barrios / Ida De Bonis
  • Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza, Università di Roma, Italy
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ María Medina / Ireneo Peral
Published Online: 2015-06-11 | DOI: https://doi.org/10.1515/math-2015-0038


The aim of this paper is to study the solvability of the problem

where Ω is a bounded smooth domain of RN, N > 2s, M ε {0, 1}, 0 < s < 1, γ > 0, λ > 0, p > 1 and f is a nonnegative function. We distinguish two cases:

– For M = 0, we prove the existence of a solution for every γ > 0 and λ > 0.

A1 – For M = 1, we consider f ≡ 1 and we find a threshold ʌ such that there exists a solution for every 0 < λ < ʌ ƒ, and there does not for λ > ʌ ƒ

Keywords: Fractional Laplacian; Solvability of elliptic equations; Existence and multiplicity


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About the article

Received: 2014-12-16

Accepted: 2015-05-28

Published Online: 2015-06-11

Citation Information: Open Mathematics, Volume 13, Issue 1, ISSN (Online) 2391-5455, DOI: https://doi.org/10.1515/math-2015-0038.

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©2015 Begoña Barrios et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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