Semilinear problems for the fractional laplacian with a singular nonlinearity

By Begoña Barrios, I. de Bonis, María Medina, I. Peral. 2015

116 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/d97451b272d66b79c6715c535cd93022ad692712

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In Applied Mathematics

In Numerical Analysis

Citations in the corpus

Mixed local and nonlocal Sobolev inequalities with extremal and associated quasilinear singular elliptic problems (2021, methodology): “The perturbed singular case is investigated by Barrios-De Bonis-Medina-Peral [10], Adimurthi-Giacomoni-Santra [1] for p = 2; MukherjeeSreenadh [57] in the quasilinear case and the references therein.”
Combined effects in mixed local–nonlocal stationary problems (2021, background): “Turning to the nonlocal case, the singular problems have been investigated more recently and there are few works in the literature, in particular, with the fractional Laplacian (−∆) and related to Lazer-Mckeena type problem (see for instance [4, 7, 8, 10]).”
Nonlocal problems with singular nonlinearity (2016, methodology): “Such a procedure has been investigated in the nonlocal case for p = 2 in [2], where a slightly different very weak notion of solution is considered that is allowed by the fact that the operator is linear and admits a double integration by parts.”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, unknown): “In [5] the authors the singular problem (−∆)u = λ f(x) uγ +Mu, u > 0 in Ω, u = 0 in R \ Ω, where n > 2s, M ≥ 0, 0 < s < 1, γ > 0, λ > 0, 1 < p < 2s − 1 and f ∈ L m(Ω), m ≥ 1 is a nonnegative function.”