Bifurcation and multiplicity results for critical fractionalp-Laplacian problems

DOI10.1002/mana.201400259zbMath1336.35050arXiv1407.8061OpenAlexW1942587350MaRDI QIDQ2792258

Perera, Kanishka, Marco Squassina, Yingchen Yang

Publication date: 8 March 2016

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.8061

zbMATH Keywords

critical nonlinearitycohomological indexpseudo-indexnew abstract critical point theorem

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Bifurcations in context of PDEs (35B32) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items

Nonlocal p-Kirchhoff equations with singular and critical nonlinearity terms ⋮ Existence, multiplicity and regularity of solutions for the fractional $p$-Laplacian equation ⋮ Bifurcation results for the critical Choquard problem involving fractional \(p\)-Laplacian operator ⋮ Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ Fractional \(p\)-Laplacian equations with subcritical and critical exponential growth without the Ambrosetti-Rabinowitz condition ⋮ Existence results for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities ⋮ Five solutions for the fractional \(p\)-Laplacian with noncoercive energy ⋮ Positive solutions of \(p\)-Laplacian fractional differential equations with fractional derivative boundary condition ⋮ Unnamed Item ⋮ Critical nonlocal systems with concave-convex powers ⋮ Schrödinger equations involving fractional p-Laplacian with supercritical exponent ⋮ Existence and multiplicity results for the fractional p-Laplacian equation with Hardy-Sobolev exponents ⋮ Multiplicity results for degenerate fractional \(p\)-Laplacian problems with critical growth ⋮ Multiplicity results for a nonlocal fractional problem ⋮ Existence of a weak solution for the fractional \(p\)-Laplacian equations with discontinuous nonlinearities via the Berkovits-Tienari degree theory ⋮ Sign changing solutions of \(p\)-fractional equations with concave-convex nonlinearities ⋮ The positive solutions to a quasi-linear problem of fractional \(p\)-Laplacian type without the Ambrosetti-Rabinowitz condition ⋮ Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem ⋮ Optimal solvability for a nonlocal problem at critical growth ⋮ \(p\)-fractional Hardy-Schrödinger-Kirchhoff systems with critical nonlinearities ⋮ Existence of solutions for fractional p&q-Laplacian system involving critical sandwich-type nonlinearities ⋮ Multiplicity of solutions for fractional p -Laplacian equation with indefinite nonlinearity ⋮ On the logistic equation for the fractional p‐Laplacian ⋮ A perturbed fractional p-Kirchhoff problem with critical nonlinearity ⋮ A general perturbation theorem with applications to nonhomogeneous critical growth elliptic problems ⋮ The effect of the domain topology on the number of positive solutions for fractional \(p\)-Laplacian equation with critical growth ⋮ Existence and bifurcation of positive solutions for fractional p$$ p $$‐Kirchhoff problems ⋮ EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N ⋮ Degenerate Kirchhoff \((p, q)\)-fractional systems with critical nonlinearities ⋮ Unnamed Item ⋮ A note on the combination between local and nonlocal p-Laplacian operators ⋮ Existence of nontrivial solutions for fractional differential equations with $p$-Laplacian ⋮ Multiple solutions for the fractional \(p\)-Laplacian equation with Hardy-Sobolev exponents ⋮ Some results on fractional $m$-point boundary value problems ⋮ The Brezis-Nirenberg problem for the fractional \(p\)-Laplacian ⋮ On the existence of ground state solutions to critical growth problems nonresonant at zero ⋮ On a fractional \(p\)-Laplacian problem with discontinuous nonlinearities ⋮ Unnamed Item ⋮ Multiplicity of solutions for a class of fractional Choquard-Kirchhoff equations involving critical nonlinearity ⋮ Combined effects of Choquard and singular nonlinearities in fractional Kirchhoff problems ⋮ Multiplicity results of a nonlocal problem involving concave-convex nonlinearities ⋮ Classification of positive solutions to the critical fractional Choquard equation in ⋮ Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities ⋮ Three solutions for a nonlocal problem with critical growth ⋮ Kirchhoff equations with Choquard exponential type nonlinearity involving the fractional Laplacian ⋮ Fractional \(p\)-Laplacian problems with Hardy terms and critical exponents ⋮ Ground state solutions for fractional \(p\)-Kirchhoff equation with subcritical and critical exponential growth ⋮ A singular system involving the fractional \(p\)-Laplacian operator via the Nehari manifold approach ⋮ Critical Kirchhoff \(p(\cdot) \& q(\cdot)\)-fractional variable-order systems with variable exponent growth ⋮ Multiple of solutions for nonlocal elliptic equations with critical exponent driven by the Fractional \(p\)-Laplacian of order \(s\) ⋮ Existence and multiplicity of solutions for a fractional \(p\)-Laplacian equation with perturbation ⋮ Critical Kirchhoff-Choquard system involving the fractional \(p\)-Laplacian operator and singular nonlinearities ⋮ Unnamed Item ⋮ REGULARITY AND MULTIPLICITY OF SOLUTIONS FOR A NONLOCAL PROBLEM WITH CRITICAL SOBOLEV-HARDY NONLINEARITIES ⋮ Existence of solutions for critical fractional p&q-Laplacian system ⋮ Existence and multiplicity of solutions for fractional Laplacian system ⋮ The obstacle problem at zero for the fractional \(p\)-Laplacian

Cites Work

• Existence results for fractional \(p\)-Laplacian problems via Morse theory
• Local behavior of fractional \(p\)-minimizers
• Nonlocal Harnack inequalities
• On some critical problems for the fractional Laplacian operator
• Hitchhiker's guide to the fractional Sobolev spaces
• Global Hölder regularity for the fractional \(p\)-Laplacian
• Bifurcation and multiplicity results for critical \(p\)-Laplacian problems
• A critical fractional Laplace equation in the resonant case
• Hölder estimates for viscosity solutions of equations of fractional \(p\)-Laplace type
• The Brezis-Nirenberg type problem involving the square root of the Laplacian
• Stability of variational eigenvalues for the fractional \(p\)-Laplacian
• Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems
• Bifurcation and multiplicity results for nonlinear elliptic problems involving critical Sobolev exponents
• A note on the problem \(-\Delta u=\lambda u+u\,| u| ^{2^*-2}\)
• An existence result for nonliner elliptic problems involving critical Sobolev exponent
• Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
• A note on problems involving critical Sobolev exponents
• Multiplicity of positive solutions for some quasilinear elliptic equations in \(\mathbb{R}^N\) with critical Sobolev exponent
• Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations
• Nontrivial critical groups in \(p\)-Laplacian problems via the Yang index
• Quasilinear Dirichlet problems in \(\mathbb R^N\) with critical growth.
• Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
• A Brezis-Nirenberg result for non-local critical equations in low dimension
• Nonlocal equations with measure data
• \(p\)-Laplacian problems where the nonlinearity crosses an eigenvalue
• Fractional eigenvalues
• Non-local Diffusions, Drifts and Games
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Quasilinear elliptic equations involving critical Sobolev exponents
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Multiplicity of Solutions for Elliptic Problems with Critical Exponent or with a Nonsymmetric Term
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• A multiplicity result for quasilinear elliptic equations involving critical sobolev exponents
• Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponents
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
• On Critical Point Theory for Indefinite Functionals in The Presence of Symmetries
• The Brezis-Nirenberg result for the fractional Laplacian