Existence results for Schrödinger-Choquard-Kirchhoff equations involving the fractional \(p\)-Laplacian

DOI10.1515/acv-2016-0049zbMath1431.35233OpenAlexW2736508307MaRDI QIDQ2311869

Binlin Zhang, Mingqi Xiang, Patrizia Pucci

Publication date: 4 July 2019

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2016-0049

zbMATH Keywords

variational methodscritical exponentfractional \(p\)-LaplacianSchrödinger-Choquard-Kirchhoff type

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

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Existence of global solutions to a quasilinear Schrödinger equation with general nonlinear optimal control conditions ⋮ Solutions for nonhomogeneous fractional \((p, q)\)-Laplacian systems with critical nonlinearities ⋮ Classification of stable solutions to a fractional singular elliptic equation with weight ⋮ Multiple solutions for critical Choquard-Kirchhoff type equations ⋮ Existence of nontrivial solutions for Schrödinger-Kirchhoff type equations involving the fractional \(p\)-Laplacian and local nonlinearity ⋮ Fractional Kirchhoff-Choquard equations involving upper critical exponent and general nonlinearity ⋮ Degenerate fractional Kirchhoff-type system with magnetic fields and upper critical growth ⋮ Existence and concentration of ground-states for fractional Choquard equation with indefinite potential ⋮ Small linear perturbations of fractional Choquard equations with critical exponent ⋮ Ground state solutions for fractional Schrödinger–Choquard–Kirchhoff type equations with 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\& q(\cdot)\)-fractional variable-order systems with variable exponent growth ⋮ Critical Kirchhoff-Choquard system involving the fractional \(p\)-Laplacian operator and singular nonlinearities ⋮ On a class of Kirchhoff-Choquard equations involving variable-order fractional \(p(\cdot)\)-Laplacian and without Ambrosetti-Rabinowitz type condition ⋮ Ground state solution ofp-Laplacian equation with finite many critical nonlinearities ⋮ A Liouville-type theorem for fractional elliptic equation with exponential nonlinearity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical stationary Kirchhoff equations in \(\mathbb R^N\) involving nonlocal operators
• Local behavior of fractional \(p\)-minimizers
• Existence theorems for entire solutions of stationary Kirchhoff fractional \(p\)-Laplacian equations
• Nonlocal Harnack inequalities
• Hitchhiker's guide to the fractional Sobolev spaces
• Existence of solutions for Kirchhoff type problem involving the non-local fractional \(p\)-Laplacian
• The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations in \(\mathbb R^N\)
• Stationary Kirchhoff problems involving a fractional elliptic operator and a critical nonlinearity
• Multiplicity of solutions for \(p(x)\)-polyharmonic elliptic Kirchhoff equations
• On nonlocal Choquard equations with Hardy-Littlewood-Sobolev critical exponents
• Existence of semiclassical ground state solutions for a generalized Choquard equation
• Multiple solutions for nonhomogeneous Schrödinger-Kirchhoff type equations involving the fractional \(p\)-Laplacian in \(\mathbb R^N\)
• Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity
• Functional analysis, Sobolev spaces and partial differential equations
• Global solvability for the degenerate Kirchhoff equation with real analytic data
• The Brezis-Nirenberg type critical problem for the nonlinear Choquard equation
• Entire solutions for critical \(p\)-fractional Hardy Schrödinger Kirchhoff equations
• Nonlocal equations with measure data
• Infinitely many solutions for a fractional Kirchhoff type problem via fountain theorem
• A note on Kirchhoff-type equations with Hartree-type nonlinearities
• Existence and multiplicity of entire solutions for fractional \(p\)-Kirchhoff equations
• Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
• A critical Kirchhoff type problem involving a nonlocal operator
• Critical growth fractional elliptic problem with singular nonlinearities
• Infinitely many solutions for the stationary Kirchhoff problems involving the fractionalp-Laplacian
• Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field
• Non-local Diffusions, Drifts and Games
• Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent
• Fractional Elliptic Problems with Critical Growth in the Whole of ℝn
• Variational Methods for Nonlocal Fractional Problems
• Quantum computation, entanglement and state reduction
• The Choquard equation and related questions
• Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
• Existence and multiplicity results for some superlinear elliptic problems on R^N
• On fractional Choquard equations
• Multiplicity results for the non-homogeneous fractional p -Kirchhoff equations with concave–convex nonlinearities
• An Extension Problem Related to the Fractional Laplacian

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