A Brezis-Nirenberg splitting approach for nonlocal fractional equations

DOI10.1016/j.na.2014.10.025zbMath1383.35244OpenAlexW1984009851MaRDI QIDQ2349082

Raffaella Servadei, Giovanni Molica Bisci

Publication date: 16 June 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2014.10.025

zbMATH Keywords

variational methodscritical point theorynonlocal problemsfractional Laplacianintegrodifferential operators

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence of solutions for minimax problems (49J35) Boundary value problems for PDEs with pseudodifferential operators (35S15) Singular nonlinear integral equations (45G05) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

Related Items (22)

Critical growth fractional elliptic systems with exponential nonlinearity ⋮ The Brezis-Nirenberg problem for the fractional Laplacian with mixed Dirichlet-Neumann boundary conditions ⋮ Existence, nonexistence, and multiple results for the fractional \(p\)-Kirchhoff-type equation in \(\mathbb R^N\) ⋮ On Dirichlet problem for fractional \(p\)-Laplacian with singular non-linearity ⋮ Ground state solutions of scalar field fractional Schrödinger equations ⋮ Fractional Choquard equation with critical nonlinearities ⋮ Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups ⋮ Radially symmetric sign-definite solutions for a class of nonlocal Schrödinger equations ⋮ Tempered random attractors of a non-autonomous non-local fractional equation driven by multiplicative white noise ⋮ A problem involving a nonlocal operator ⋮ Asymptotical dynamics for non-autonomous stochastic equations driven by a non-local integro-differential operator of fractional type ⋮ Existence of positive solutions for a singular elliptic problem with critical exponent and measure data ⋮ Bounded resonant problems driven by fractional Laplacian ⋮ Multiple solutions of a nonlocal system with singular nonlinearities ⋮ Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators ⋮ Positive solutions of fractional elliptic equation with critical and singular nonlinearity ⋮ Resonant problems for fractional Laplacian ⋮ Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity ⋮ Nonlinear fractional equations with supercritical growth ⋮ Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero ⋮ A singular system involving the fractional \(p\)-Laplacian operator via the Nehari manifold approach ⋮ On a nonlinear elliptic fractional problem under mixed boundary condition: effect of the geometry of the domain

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