The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis-Nirenberg problem

DOI10.1007/s00030-018-0543-5zbMath1407.35201arXiv1802.09322OpenAlexW2963079593WikidataQ129065214 ScholiaQ129065214MaRDI QIDQ1729785

Julián Fernández Bonder, Nicolas Saintier, Analia Silva

Publication date: 28 February 2019

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.09322

zbMATH Keywords

unbounded domainsconcentration-compactness principlefractional elliptic-type problems

Mathematics Subject Classification ID

Singular nonlinear integral equations (45G05) Rings and algebras of continuous, differentiable or analytic functions (46E25) Fractional partial differential equations (35R11)

Related Items (22)

Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ Fractional elliptic problems with nonlinear gradient sources and measures ⋮ Existence and multiplicity results for fractional Schrödinger equation with critical growth ⋮ Multiplicity of positive solutions to a critical fractional equation with Hardy potential and concave–convex nonlinearities ⋮ Unnamed Item ⋮ Existence and multiplicity of solutions for critical nonlocal equations with variable exponents ⋮ The concentration-compactness principle for the nonlocal anisotropic \(p\)-Laplacian of mixed order ⋮ The effect of the domain topology on the number of positive solutions for fractional \(p\)-Laplacian equation with critical growth ⋮ The Brézis-Nirenberg equation for the \((m,p)\) Laplacian in the whole space ⋮ Existence results for fractional Brezis-Nirenberg type problems in unbounded domains ⋮ The Brezis–Nirenberg problem for fractional systems with Hardy potentials ⋮ On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces ⋮ Solutions with various structures for semilinear equations in \(\mathbb{R}^n\) driven by fractional Laplacian ⋮ Existence of solutions to elliptic problems with fractional p-Laplacian and multiple critical nonlinearities in the entire space \(\mathbb{R}^N\) ⋮ Compact Sobolev-Slobodeckij embeddings and positive solutions to fractional Laplacian equations ⋮ Asymptotic behaviour of ground state solutions for the fractional Hénon equation ⋮ Extremals in Hardy-Littlewood-Sobolev inequalities for stable processes ⋮ The concentration-compactness principles for \(W^{s,p(\cdot,\cdot)}(\mathbb{R}^N)\) and application ⋮ Existence for fractional \((p,q)\) systems with critical and Hardy terms in \(\mathbb{R}^N\) ⋮ Critical \(p(x)\)-Kirchhoff problems involving variable singular exponent ⋮ Existence of solutions to fractional \(p\)-Laplacian systems with homogeneous nonlinearities of critical Sobolev growth ⋮ Entire solutions for some critical equations in the Heisenberg group

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