Solutions for fractional Schrödinger equation involving critical exponent via local Pohozaev identities

DOI10.1515/ans-2019-2067zbMath1432.35221OpenAlexW2986365599MaRDI QIDQ2305522

Ting Liu, Jianjun Nie, Yuxia Guo

Publication date: 11 March 2020

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2019-2067

zbMATH Keywords

critical exponentinfinitely many solutionsfractional Schrödinger equationlocal Pohozaev identities

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Nonlinear elliptic equations (35J60) Fractional partial differential equations (35R11)

Related Items (11)

Construct new type solutions for the fractional Schrödinger equation ⋮ Existence and multiplicity results for fractional Schrödinger equation with critical growth ⋮ Non-degeneracy of bubbling solutions for fractional Schrödinger equation and its application ⋮ Non-degeneracy of the bubble solutions for the Hénon equation and applications ⋮ On the Neumann problem for fractional semilinear elliptic equations arising from Keller–Segel model ⋮ Asymptotic non-degeneracy of the multipeak solution for the supercritical Hénon equation ⋮ Local uniqueness and non-degeneracy of bubbling solution for critical Hamiltonian system ⋮ Non-degeneracy of the bubble solutions for the fractional prescribed curvature problem and applications ⋮ Large number of bubble solutions for a fractional elliptic equation with almost critical exponents ⋮ Large energy bubble solutions for Schrödinger equation with supercritical growth ⋮ Multiple high energy solutions for fractional Schrödinger equation with critical growth

Cites Work

• On some critical problems for the fractional Laplacian operator
• Hitchhiker's guide to the fractional Sobolev spaces
• The Brezis-Nirenberg type problem involving the square root of the Laplacian
• A Harnack inequality for fractional Laplace equations with lower order terms
• Infinitely many non-radial solutions for the prescribed curvature problem of fractional operator
• The scalar-curvature problem on the standard three-dimensional sphere
• Mountain pass solutions for non-local elliptic operators
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• Infinitely many solutions for the prescribed scalar curvature problem on \(\mathbb S^N\)
• Positive solutions of nonlinear problems involving the square root of the Laplacian
• On conformal scalar curvature equations in \({\mathbb{R}}^ n\)
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Estimate of the conformal scalar curvature equation via the method of moving planes. II
• Two-bubble solutions in the super-critical Bahri-Coron's problem
• Concentration of solutions for the scalar curvature equation on \(\mathbb{R}^n\)
• Prescribing scalar curvature on \(S^ N\). I: A priori estimates.
• Multiplicity of positive solutions for a class of fractional Schrödinger equations via penalization method
• Construction of solutions via local Pohozaev identities
• Periodic solutions for critical fractional problems
• On the scalar curvature equation \(-\Delta u = (1+\varepsilon K)u ^{(N+2)/(N-2)}\) in \({\mathbb R}^N\)
• Prescribed scalar curvature on the \(n\)-sphere
• Infinitely many solutions for the prescribed curvature problem of polyharmonic operator
• Construction of solutions for the polyharmonic equation via local Pohozaev identities
• Equations involving fractional Laplacian operator: compactness and application
• Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials
• Concentrating standing waves for the fractional nonlinear Schrödinger equation
• Ground states for a fractional scalar field problem with critical growth.
• Local uniqueness and periodicity for the prescribed scalar curvature problem of fractional operator in \({\mathbb {R}}^{N}\)
• Infinitely many solutions for cubic nonlinear Schrödinger equations in dimension four
• Solutions for conformally invariant fractional Laplacian equations with multi-bumps centered in lattices
• Nonlinear equations for fractional Laplacians. I: Regularity, maximum principles, and Hamiltonian estimates
• On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
• Solutions of the fractional Allen–Cahn equation which are invariant under screw motion
• A concave—convex elliptic problem involving the fractional Laplacian
• Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
• Regularity of the obstacle problem for a fractional power of the laplace operator
• Lévy Processes and Stochastic Calculus
• Concentration phenomena for a fractional Schrödinger‐Kirchhoff type equation
• Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness
• Non-uniqueness of positive ground states of non-linear Schrödinger equations
• Local uniqueness and periodicity induced by concentration
• An Extension Problem Related to the Fractional Laplacian
• The scalar curvature equation on \(\mathbb R^N\)

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