On a Nirenberg-type problem involving the square root of the Laplacian

Abdelhedi, Wael; Chtioui, Hichem

doi:10.1016/j.jfa.2013.08.005

Cited by 31 publications

(55 citation statements)

References 33 publications

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“…[15,16,23,24,26], but their methods differ from the our. Note however that in [1] and [17] the authors used, as we do, the theory of critical points at infinity, but they conclude in different ways from us. More particularely in [17] Chen, Liu and Zheng addressed the problem (1.1) using the same framework that ours; they established an Euler-Hopf-type formula, and obtained some existence results under Bahri-Coron-type assumptions.…”

Section: Introductionmentioning

confidence: 75%

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Bahri invariants for fractional Nirenberg-type flows

Yacoub

2017

Arab. J. Math.

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This paper is concerned with prescribing the fractional Q-curvature on the unit sphere S n endowed with its standard conformal structure g 0 , n ≥ 4. Since the associated variational problem is noncompact, we approach this issue with techniques passed by Abbas Bahri, as the well known theory of critical points at infinity, as well as some lesser known topological invariants that appear here as criteria for existence results. Mathematics Subject Classification

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Section: Introductionmentioning

confidence: 75%

“…1 In conformal geometry the Nirenberg problem is the well-known problem of prescribing the scalar (resp. Gauss) curvature on the sphere S n for n ≥ 3 (resp.…”

Section: Introductionmentioning

confidence: 99%

Bahri invariants for fractional Nirenberg-type flows

Yacoub

2017

Arab. J. Math.

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“…See e.g. [1,2,6,7,19,20,22,23,28,38,41] and references therein where such results are obtained with various types of f .…”

Section: Introductionmentioning

confidence: 93%

Minimal energy solutions to the fractional Lane–Emden system: Existence and singularity formation

Choi

Kim

2019

Rev. Mat. Iberoam.

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This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain Ωunder the assumption that the subcritical pair (p, q) approaches to the critical Sobolev hyperbola. If p = 1, the above problem is reduced to the subcritical higher-order fractional Lane-Emden equation with the Navier boundary condition (−∆) s u = u n+2s n−2s −ǫ in Ω and u = (−∆) s 2 u = 0 for 1 < s < 2.The main objective of this paper is to deduce the existence of minimal energy solutions, and to examine their (normalized) pointwise limits provided that Ω is convex. As a by-product of our study, a new approach for the existence of an extremal function for the Hardy-Littlewood-Sobolev inequality is provided.

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“…1 Furthermore, it was shown in [20,42,44] that if a suitable decay assumption is imposed, then {w λ,ξ : λ > 0, ξ ∈ R N } is the set of all solutions for the problem…”

Section: Sharp Sobolev and Trace Inequalitiesmentioning

confidence: 99%

“…For the results of particular equations, we refer to papers on the Schrödinger equations [3,22,28,32], the Allen-Cahn equations [12,13], the Fisher-KPP equations [8,11], the Nirenberg problem [1,39,40], and the Yamabe problem [24,34,35,41], respectively. Also, Brezis-Nirenberg-type problems have been tackled in [6,27,60].…”

Section: Introductionmentioning

confidence: 99%

Classification of finite energy solutions to the fractional Lane–Emden–Fowler equations with slightly subcritical exponents

Choi

Kim

2016

Annali di Matematica

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We study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined in terms of either the spectra of the Dirichlet Laplacian or the integral representation. As a consequence, we classify the asymptotic behavior of all finite energy solutions. Our method also provides a simple and unified approach to deal with the classical (local) LaneEmden-Fowler equation for any dimension >2.

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On a Nirenberg-type problem involving the square root of the Laplacian

Cited by 31 publications

References 33 publications

Bahri invariants for fractional Nirenberg-type flows

Bahri invariants for fractional Nirenberg-type flows

Minimal energy solutions to the fractional Lane–Emden system: Existence and singularity formation

Classification of finite energy solutions to the fractional Lane–Emden–Fowler equations with slightly subcritical exponents

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