The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate

DOI10.1016/j.jfa.2017.02.026zbMath1386.35052arXiv1612.02194OpenAlexW2560578211MaRDI QIDQ527390

Silvia Cingolani, Denis Bonheure, Jean Van Schaftingen

Publication date: 11 May 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.02194

zbMATH Keywords

asymptoticslogarithmic Choquard equationpositive ground state solution

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items (25)

Minimizers of the planar Schrödinger–Newton equations ⋮ Elliptic problem driven by different types of nonlinearities ⋮ Existence of solutions for a perturbed problem with logarithmic potential in \(\mathbb{R}^2\) ⋮ Quasilinear logarithmic Choquard equations with exponential growth in \(\mathbb{R}^N\) ⋮ Multiplicity and concentration of solutions for Choquard equation via Nehari method and pseudo-index theory ⋮ Existence and stability of standing waves for the Choquard equation with partial confinement ⋮ Trudinger–Moser‐type inequality with logarithmic convolution potentials ⋮ Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case ⋮ Existence of positive solution for a planar Schrödinger-Poisson system with exponential growth ⋮ Multi-peak solutions for nonlinear Choquard equation in the plane ⋮ Groundstates for Choquard type equations with weighted potentials and Hardy-Littlewood-Sobolev lower critical exponent ⋮ On a planar Choquard equation involving exponential critical growth ⋮ On existence and concentration behavior of positive ground state solutions for a class of fractional Schrödinger-Choquard equations ⋮ Ground state solutions for planar Schrödinger-Poisson system involving subcritical and critical exponential growth with convolution nonlinearity ⋮ On a logarithmic Hartree equation ⋮ Groundstates of the Choquard equations with a sign-changing self-interaction potential ⋮ Schrödinger-Newton equations in dimension two via a Pohozaev-Trudinger log-weighted inequality ⋮ Existence of solutions to the logarithmic Choquard equations in high dimensions ⋮ Concentration phenomena for the Schrödinger-Poisson system in \(\mathbb{R}^2\) ⋮ Stationary Waves with Prescribed $L^2$-Norm for the Planar Schrödinger--Poisson System ⋮ Existence and multiplicity of solutions for the fractional p-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth ⋮ The planar Schrödinger–Poisson system with a positive potential^* ⋮ The Choquard logarithmic equation involving a nonlinearity with exponential growth ⋮ On a quasilinear logarithmic \(N\)-dimensional equation involving exponential growth ⋮ Positive solutions for a planar Schrödinger-Poisson system with prescribed mass

Uses Software

• DLMF

Cites Work

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