Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian

DOI10.1007/s00526-013-0706-5zbMath1317.35285OpenAlexW1977796932MaRDI QIDQ488124

Yuanhong Wei, Xifeng Su

Publication date: 23 January 2015

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-013-0706-5

zbMATH Keywords

existencemultiplicity of solutionsfractional Laplacian

Mathematics Subject Classification ID

Fractional partial differential equations (35R11) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (46)

Existence, multiplicity and regularity of solutions for the fractional $p$-Laplacian equation ⋮ Multiplicity of solutions for a class of fractional \(p\)-Kirchhoff system with sign-changing weight functions ⋮ Multiplicity and concentration of positive solutions for fractional \(p\)-Laplacian problem involving concave-convex nonlinearity ⋮ Unnamed Item ⋮ The Nehari manifold for fractional systems involving critical nonlinearities ⋮ On the superlinear problems involving the fractional Laplacian ⋮ Multiple positive solutions for a fractional elliptic system with critical nonlinearities ⋮ Multiplicity of positive solutions for critical fractional equation involving concave-convex nonlinearities and sign-changing weight functions ⋮ The Nehari manifold for a fractional Laplacian equation involving critical nonlinearities ⋮ Existence of solutions for nonlocal supercritical elliptic problems ⋮ Multiplicity of positive solutions for critical fractional Kirchhoff type problem with concave-convex nonlinearity ⋮ Generalized solutions for nonlocal elliptic equations and systems with nonlinear singularities ⋮ Existence and multiplicity results for resonant fractional boundary value problems ⋮ Schrödinger-Kirchhoff-Hardy \(p \)-fractional equations without the Ambrosetti-Rabinowitz condition ⋮ Existence of positive radial solutions for nonlinear elliptic equations with gradient terms in an annulus ⋮ On a class of non-local elliptic equations with asymptotically linear term ⋮ The Nehari manifold for a fractional \(p\)-Laplacian system involving concave-convex nonlinearities ⋮ Existence results and bifurcation for nonlocal fractional problems with critical Sobolev exponent ⋮ EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N ⋮ Regularity and multiplicity results for fractional (p,q)-Laplacian equations ⋮ Multiple positive solutions for a fractional Laplacian system with critical nonlinearities ⋮ Unnamed Item ⋮ A problem involving a nonlocal operator ⋮ A note on homoclinic solutions of (p,q)-Laplacian difference equations ⋮ The Nehari manifold for nonlocal elliptic operators involving concave-convex nonlinearities ⋮ Multiplicity of nontrivial solutions of a class of fractional \(p\)-Laplacian problem ⋮ Multiplicity and concentration of positive solutions to the fractional Kirchhoff type problems involving sign-changing weight functions ⋮ Vector solutions with clustered peaks for nonlinear fractional Schrödinger systems in \(\mathbb {R}^{N}\) ⋮ Existence and multiplicity of positive solutions for the fractional Laplacian under subcritical or critical growth ⋮ Multiple solutions for a class of fractional quasi-linear equations with critical exponential growth in ℝ^N ⋮ Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains ⋮ On a class of Kirchhoff equations involving an anisotropic operator and potential ⋮ A limiting problem for local/non-local \(p\)-Laplacians with concave-convex nonlinearities ⋮ On some fractional equations with convex-concave and logistic-type nonlinearities ⋮ Existence and stability for a nonlinear coupled \(p\)-Laplacian system of fractional differential equations ⋮ Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity ⋮ Infinitely many solutions for non-local elliptic non-degeneratep-Kirchhoff equations with critical exponent ⋮ Nonlinear fractional equations with supercritical growth ⋮ Existence of multiple solutions for a fractional \(p\)-Laplacian system with concave-convex term ⋮ INFINITELY MANY SOLUTIONS FOR NONLOCAL SYSTEMS INVOLVING FRACTIONAL LAPLACIAN UNDER NONCOMPACT SETTINGS ⋮ Multiple of solutions for nonlocal elliptic equations with critical exponent driven by the Fractional \(p\)-Laplacian of order \(s\) ⋮ Regularity results for solutions of mixed local and nonlocal elliptic equations ⋮ Ground states for fractional linear coupled systems via profile decomposition ^* ⋮ Nonexistence results for some nonlinear nonlocal elliptic inequalities with variable exponents ⋮ INFINITELY MANY SOLUTIONS FOR CRITICAL FRACTIONAL EQUATION WITH SIGN-CHANGING WEIGHT FUNCTION ⋮ Two disjoint and infinite sets of solutions for a concave-convex critical fractional Laplacian equation

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