Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity

From MaRDI portal

Publication:495262

Jump to:navigation, search

DOI10.1016/j.na.2015.06.014zbMath1323.35015arXiv1410.6762OpenAlexW1843205648MaRDI QIDQ495262

Alessio Fiscella, Giuseppina Autuori, Patrizia Pucci

Publication date: 9 September 2015

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

Full work available at URL: https://arxiv.org/abs/1410.6762

zbMATH Keywords

existence of solutions variational methods fractional Sobolev spaces critical nonlinearities stationary Kirchhoff Dirichlet problems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elliptic equations (35J60) Existence of solutions for minimax problems (49J35) Boundary value problems for PDEs with pseudodifferential operators (35S15) Variational methods for second-order elliptic equations (35J20) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items

Infinitely many sign-changing solutions for nonlinear fractional Kirchhoff equations ⋮ Global existence and asymptotic behavior of solutions to fractional ( p , q )-Laplacian equations ⋮ Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions ⋮ A multiplicity result for a fractional Kirchhoff equation in ℝN with a general nonlinearity ⋮ Fractional Kirchhoff-Choquard equations involving upper critical exponent and general nonlinearity ⋮ Unnamed Item ⋮ Ground state solutions for fractional Schrödinger–Choquard–Kirchhoff type equations with critical growth ⋮ Anomalous pseudo-parabolic Kirchhoff-type dynamical model ⋮ Fractional Kirchhoff equation with a general critical nonlinearity ⋮ Multiplicity results for stationary Kirchhoff problems involving fractional elliptic operator and critical nonlinearity in RN ⋮ On critical variable-order Kirchhoff type problems with variable singular exponent ⋮ A fractional Kirchhoff problem involving a singular term and a critical nonlinearity ⋮ \(p\)-fractional Hardy-Schrödinger-Kirchhoff systems with critical nonlinearities ⋮ On the critical Choquard-Kirchhoff problem on the Heisenberg group ⋮ Existence of multiple solutions for fractional \(p\)-Kirchhoff equation with critical Sobolev exponent ⋮ Infinitely many positive multi-bump solutions for fractional Kirchhoff equations ⋮ Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term ⋮ On nonlinear perturbations of a periodic integrodifferential Kirchhoff equation with critical exponential growth ⋮ Existence and multiplicity of solutions for critical nonlocal equations with variable exponents ⋮ Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity ⋮ Sign-changing solution for a generalized Kirchhoff problem in the fractional Orlicz-Sobolev space with nonsmooth nonlinearity ⋮ Existence and multiplicity of solutions for a mixed local-nonlocal system with logarithmic nonlinearities ⋮ Multiple solutions for a Kirchhoff-type problem with vanishing nonlocal term and fractional \(p\)-Laplacian ⋮ Critical Kirchhoff equations involving the p-sub-Laplacians operators on the Heisenberg group ⋮ Ground state solutions for a class of fractional Kirchhoff equations with critical growth ⋮ Existence results for Kirchhoff–type superlinear problems involving the fractional Laplacian ⋮ Fractional weighted \(p\)-Kirchhoff equations with general nonlinearity ⋮ A nonlocal type problem involving a mixed local and nonlocal operator ⋮ A Moser-Trudinger type inequality on the Orlicz fractional space ⋮ On a nonlocal elliptic system of Hardy‐Kirchhoff type with critical exponents ⋮ Existence results for a critical fractional equation ⋮ On the \(p\)-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and the Hardy-Littlewood-Sobolev nonlinearity ⋮ Lower semicontinuity of Kirchhoff-type energy functionals and spectral gaps on (sub)Riemannian manifolds ⋮ Kirchhoff-type fractional Laplacian problems with critical and singular nonlinearities ⋮ Existence of solutions for critical fractional Kirchhoff problems ⋮ Unnamed Item ⋮ A critical fractional Choquard–Kirchhoff problem with magnetic field ⋮ Ground state sign-changing solutions for fractional Kirchhoff equations in bounded domains ⋮ Infinitely many solutions for Kirchhoff-type variable-order fractional Laplacian problems involving variable exponents ⋮ Critical fractional p-Kirchhoff type problem with a generalized Choquard nonlinearity ⋮ Combined effects for fractional Schrödinger–Kirchhoff systems with critical nonlinearities ⋮ SOLUTIONS FOR THE KIRCHHOFF TYPE EQUATIONS WITH FRACTIONAL LAPLACIAN ⋮ Existence and multiplicity solutions for thep–fractional Schrödinger–Kirchhoff equations with electromagnetic fields and critical nonlinearity ⋮ A critical Kirchhoff type problem involving the fractional Laplacian in ⋮ The Brezis-Nirenberg result for the Kirchhoff-type equation in dimension four ⋮ On multiplicity solutions for a non-local fractional p-Laplace equation ⋮ Solutions of stationary Kirchhoff equations involving nonlocal operators with critical nonlinearity in RN ⋮ Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity ⋮ A fractional Kirchhoff-type problem in ℝ^Nwithout the (AR) condition ⋮ Solutions of p-Kirchhoff type problems with critical nonlinearity in R N ⋮ A remark on fractionalp–Kirchhoff problems involving multiple zeros ⋮ Concentration of positive solutions for a class of fractionalp-Kirchhoff type equations ⋮ Multiplicity of solutions for a fractional p-Kirchhoff type problem with sign-changing weights function ⋮ A NON-RADIALLY SYMMETRIC SOLUTION TO A CLASS OF ELLIPTIC EQUATION WITH KIRCHHOFF TERM ⋮ Nodal solutions for double phase Kirchhoff problems with vanishing potentials ⋮ On solutions for a class of fractional Kirchhoff-type problems with Trudinger–Moser nonlinearity ⋮ Solutions for critical Kirchhoff-type problems with near resonance ⋮ Kirchhoff-Hardy fractional problems with lack of compactness ⋮ A nonhomogeneous fractional \(p\)-Kirchhoff type problem involving critical exponent in \(\mathbb{R}^N\) ⋮ Bifurcation results for the critical Choquard problem involving fractional \(p\)-Laplacian operator ⋮ Existence of ground state for fractional Kirchhoff equation with \(L^2\) critical exponents ⋮ Multiple positive solutions for a Kirchhoff type problem with a critical nonlinearity ⋮ A uniqueness result for Kirchhoff type problems with singularity ⋮ A note on Leighton's variational lemma for fractional Laplace equations ⋮ Infinitely many solutions for Schrödinger-Choquard-Kirchhoff equations involving the fractional \(p\)-Laplacian ⋮ Asymptotic behavior of the unique solution for a fractional Kirchhoff problem with singularity ⋮ Radial stationary solutions to a class of wave system as well as their asymptotical behavior ⋮ Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials ⋮ Multiple solutions for superlinear fractional problems via theorems of mixed type ⋮ Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities ⋮ Ground states for fractional Schrödinger equations involving a critical nonlinearity ⋮ Fractional Kirchhoff-type problems with exponential growth without the Ambrosetti-Rabinowitz condition ⋮ Positive solutions for a Kirchhoff-type equation with critical and supercritical nonlinear terms ⋮ Existence results for singular fractional \(p\)-Kirchhoff problems ⋮ Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations ⋮ Existence, nonexistence, and multiple results for the fractional \(p\)-Kirchhoff-type equation in \(\mathbb R^N\) ⋮ Multiplicity result for non-homogeneous fractional Schrodinger-Kirchhoff-type equations in \(\mathbb{R}^n\) ⋮ Existence of solutions for Schrödinger-Kirchhoff type problems involving nonlocal elliptic operators ⋮ Perturbation methods for nonlocal Kirchhoff-type problems ⋮ Multiplicity of solutions for the noncooperative Schrödinger-Kirchhoff system involving the fractional \(p\)-Laplacian in \({\mathbb {R}}^N\) ⋮ Degenerate Kirchhoff-type hyperbolic problems involving the fractional Laplacian ⋮ On a class of fractional Laplacian problems with variable exponents and indefinite weights ⋮ Supercritical fractional Kirchhoff type problems ⋮ Degenerate Kirchhoff-type diffusion problems involving the fractional \(p\)-Laplacian ⋮ Multiplicity of nontrivial solutions for a critical degenerate Kirchhoff type problem ⋮ Existence and multiplicity of solutions for critical Kirchhoff-type \(p\)-Laplacian problems ⋮ Fractional Schrödinger-Poisson-Kirchhoff type systems involving critical nonlinearities ⋮ Existence of solutions for fractional \(p\)-Kirchhoff type equations with a generalized Choquard nonlinearity ⋮ Entire solutions of nonlocal elasticity models for composite materials ⋮ Multiple solutions of fractional Kirchhoff equations involving a critical nonlinearity ⋮ Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension ⋮ Mathematical models for nonlocal elastic composite materials ⋮ Variational analysis for nonlocal Yamabe-type systems ⋮ Nontrivial solutions for a class of \(p\)-Kirchhoff Dirichlet problem ⋮ On an elliptic equation of \(p\)-Kirchhoff type with convection term ⋮ Approximate solution of the backward problem for Kirchhoff's model of parabolic type with discrete random noise ⋮ Fractional Hardy-Sobolev inequalities and existence results for fractional sub-Laplacians ⋮ Bifurcation and multiplicity results for critical nonlocal fractional Laplacian problems ⋮ Existence of solutions for a critical fractional Kirchhoff type problem in \(\mathbb{R}^N\) ⋮ Infinitely many solutions for problems in fractional Orlicz-Sobolev spaces ⋮ Degenerate Kirchhoff \((p, q)\)-fractional systems with critical nonlinearities ⋮ On the fractional Schrödinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity ⋮ Multiplicity of positive solutions for the Kirchhoff-type equations with critical exponent in \(\mathbb R^N\) ⋮ A critical fractional \(p\)-Kirchhoff type problem involving discontinuous nonlinearity ⋮ Fractional Kirchhoff problems with critical Trudinger-Moser nonlinearity ⋮ On critical Kirchhoff problems driven by the fractional Laplacian ⋮ A degenerate Kirchhoff-type inclusion problem with nonlocal operator ⋮ Fractional Choquard-Kirchhoff problems with critical nonlinearity and Hardy potential ⋮ Multiplicity results for a fractional Kirchhoff equation involving sign-changing weight function ⋮ Qualitative analysis for a degenerate Kirchhoff-type diffusion equation involving the fractional \(p\)-Laplacian ⋮ On a degenerate \(p\)-fractional Kirchhoff equations involving critical Sobolev-Hardy nonlinearities ⋮ \(p\)-fractional Kirchhoff equations involving critical nonlinearities ⋮ On a critical Kirchhoff-type problem ⋮ Fractional \(p\)-Kirchhoff system with sign changing nonlinearities ⋮ Multiple and nodal solutions for parametric Neumann problems with nonhomogeneous differential operator and critical growth ⋮ Near resonance for a Kirchhoff-Schrödinger-Newton system ⋮ Existence of infinitely many solutions for degenerate \(p\)-fractional Kirchhoff equations with critical Sobolev-Hardy nonlinearities ⋮ Liouville-type theorem for fractional Kirchhoff equations with weights ⋮ Periodic solutions for critical fractional problems ⋮ Ground state of Kirchhoff type fractional Schrödinger equations with critical growth ⋮ A diffusion problem of Kirchhoff type involving the nonlocal fractional \(p\)-Laplacian ⋮ Nonlocal Schrödinger-Kirchhoff equations with external magnetic field ⋮ Multiplicity of concentrating solutions for a class of fractional Kirchhoff equation ⋮ Multiplicity of solutions for a class of fractional Choquard-Kirchhoff equations involving critical nonlinearity ⋮ Existence of solutions for a bi-nonlocal fractional \(p\)-Kirchhoff type problem ⋮ Eigenvalue problems with unbalanced growth: nonlinear patterns and standing wave solutions ⋮ Superlinear Schrödinger-Kirchhoff type problems involving the fractional \(p\)-Laplacian and critical exponent ⋮ Existence and multiplicity of solutions for a superlinear Kirchhoff-type equations with critical Sobolev exponent in \(\mathbb R^N\) ⋮ High perturbations of critical fractional Kirchhoff equations with logarithmic nonlinearity ⋮ Sign-changing solutions for a fractional Kirchhoff equation ⋮ Infinitely many solutions for fractional \(p\)-Kirchhoff equations ⋮ A Hopf type lemma and the symmetry of solutions for a class of Kirchhoff equations ⋮ Existence and concentration of solutions for a Kirchhoff type problem with potentials ⋮ A uniqueness result for strong singular Kirchhoff-type fractional Laplacian problems ⋮ Nonlocal Kirchhoff problems with singular exponential nonlinearity ⋮ Ground state solutions for fractional \(p\)-Kirchhoff equation with subcritical and critical exponential growth ⋮ Existence and multiplicity solutions for the \(p\)-fractional Schrödinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity ⋮ Ground states for asymptotically periodic fractional Kirchhoff equation with critical Sobolev exponent ⋮ Combined effects of singular and exponential nonlinearities in fractional Kirchhoff problems ⋮ Existence results for Schrödinger-Choquard-Kirchhoff equations involving the fractional \(p\)-Laplacian ⋮ Editorial. Progress in nonlinear Kirchhoff problems ⋮ Existence and multiplicity of solutions for fractional Schrödinger-Kirchhoff equations with Trudinger-Moser nonlinearity ⋮ Sign-changing solutions for the stationary Kirchhoff problems involving the fractional Laplacian in \(\mathbb{R}^N\) ⋮ Nonlocal Kirchhoff problems: extinction and non-extinction of solutions ⋮ Nonlocal Kirchhoff problems with Trudinger -- Moser critical nonlinearities ⋮ Infinitely many solutions for critical degenerate Kirchhoff type equations involving the fractional \(p\)-Laplacian ⋮ Concentration of solutions for fractional Kirchhoff equations with discontinuous reaction ⋮ The existence of normalized solutions for a fractional Kirchhoff-type equation with doubly critical exponents ⋮ Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms ⋮ Infinitely many periodic solutions for a class of fractional Kirchhoff problems ⋮ Kirchhoff-type problems involving the fractional \(p\)-Laplacian on the Heisenberg group ⋮ Normalized solutions for nonlinear fractional Kirchhoff type systems ⋮ Multiple solutions for a fractional \(p\)-Kirchhoff problem with Hardy nonlinearity ⋮ Low perturbations and combined effects of critical and singular nonlinearities in Kirchhoff problems ⋮ Multiple solutions to the Kirchhoff fractional equation involving Hardy-Littlewood-Sobolev critical exponent ⋮ Existence of positive solutions for fractional Kirchhoff equation

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:495262&oldid=12374486"