Remarks about a fractional Choquard equation: ground state, regularity and polynomial decay

DOI10.1016/j.na.2017.08.005zbMath1373.35111OpenAlexW2756168145MaRDI QIDQ1675407

P. Belchior, Hamilton P. Bueno, Gilberto A. Pereira, Olímpio Hiroshi Miyagaki

Publication date: 27 October 2017

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

Full work available at URL: https://doi.org/10.1016/j.na.2017.08.005

zbMATH Keywords

variational methodsfractional Laplacianpolynomial decayChoquard equations

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Variational methods for second-order elliptic equations (35J20) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Fractional partial differential equations (35R11)

Related Items

On fractional Choquard–Kirchhoff equations with subcritical or critical nonlinearities, Symmetry of positive solutions to Choquard type equations involving the fractional \(p\)-Laplacian, The Dirichlet problem for the \(p\)-fractional Laplace equation, Existence and concentration of positive solutions for a p-fractional Choquard equation, Existence and concentration of ground-states for fractional Choquard equation with indefinite potential, On fractional Schrödinger equations with Hartree type nonlinearities, Existence of solutions for fractional \(p\)-Kirchhoff type equations with a generalized Choquard nonlinearity, Regularity results for Choquard equations involving fractional p‐Laplacian, Uniqueness of non-negative solutions to an integral equation of the Choquard type, Liouville-type theorem for a subelliptic equation with Choquard nonlinearity and weight, Liouville‐type theorems for a nonlinear fractional Choquard equation, Multi-peak solutions of a class of fractional \(p\)-Laplacian equations, Asymptotic decay of solutions for sublinear fractional Choquard equations, Multiplicity of semiclassical solutions for fractional Choquard equations with critical growth, Symmetry of solutions for a fractional p-Laplacian equation of Choquard type, Liouville‐type theorem for finite Morse index solutions to the Choquard equation involving Δ_λ‐Laplacian, Existence of solutions for fractional-Choquard equation with a critical exponential growth in \(\mathbb{R}^N\), The higher regularity and decay estimates for positive solutions of fractional Choquard equations, On the multiplicity and concentration of positive solutions for a \(p\)-fractional Choquard equation in \(\mathbb{R}^N\), Nodal solutions for pseudo-relativistic Hartree equations, Multiplicity and concentration results for a fractional Choquard equation via penalization method, Symmetry and nonexistence results for a fractional Choquard equation with weights, Critical fractional p-Kirchhoff type problem with a generalized Choquard nonlinearity, On a class of \(p(x)\)-Choquard equations with sign-changing potential and upper critical growth, Remarks about a generalized pseudo-relativistic Hartree equation, Infinitely many bound states for Choquard equations with local nonlinearities, Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional \(p\)-Laplacian, Liouville theorems for an integral equation of Choquard type, Multiplicity and concentration behaviour of solutions for a fractional Choquard equation with critical growth, Multiplicity and concentration of nontrivial nonnegative solutions for a fractional Choquard equation with critical exponent, On fractional Choquard equation with subcritical or critical nonlinearities, Pseudoindex theory and Nehari method for a fractional Choquard equation, Existence of solutions for a class of fractional coupled Choquard-type systems with potential vanishing at infinity, Liouville theorem and classification of positive solutions for a fractional Choquard type equation, Existence of ground state solutions for fractional Kirchhoff Choquard problems with critical Trudinger-Moser nonlinearity, Concentration phenomenon of solutions for fractional Choquard equations with upper critical growth, Saddle solutions for the fractional Choquard equation

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