Semilinear problems for the fractional laplacian with a singular nonlinearity

Begoña Barrios; Ida De Bonis; María Medina; Ireneo Peral

Open Mathematics (2015)

  • Volume: 13, Issue: 1
  • ISSN: 2391-5455

Abstract

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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

How to cite

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Begoña Barrios, et al. "Semilinear problems for the fractional laplacian with a singular nonlinearity." Open Mathematics 13.1 (2015): null. <http://eudml.org/doc/271034>.

@article{BegoñaBarrios2015,
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},
author = {Begoña Barrios, Ida De Bonis, María Medina, Ireneo Peral},
journal = {Open Mathematics},
keywords = {Fractional Laplacian; Solvability of elliptic equations; Existence and multiplicity},
language = {eng},
number = {1},
pages = {null},
title = {Semilinear problems for the fractional laplacian with a singular nonlinearity},
url = {http://eudml.org/doc/271034},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Begoña Barrios
AU - Ida De Bonis
AU - María Medina
AU - Ireneo Peral
TI - Semilinear problems for the fractional laplacian with a singular nonlinearity
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - null
AB - 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
LA - eng
KW - Fractional Laplacian; Solvability of elliptic equations; Existence and multiplicity
UR - http://eudml.org/doc/271034
ER -

References

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