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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 11, 2015

Semilinear problems for the fractional laplacian with a singular nonlinearity

  • Begoña Barrios , Ida De Bonis , María Medina and Ireneo Peral
From the journal Open Mathematics

Abstract

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

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Received: 2014-12-16
Accepted: 2015-5-28
Published Online: 2015-6-11

©2015 Begoña Barrios et al.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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