Liouville theorems and classification results for a nonlocal Schrödinger equation

DOI10.3934/dcds.2018236zbMath1401.35036OpenAlexW2888318201MaRDI QIDQ1791636

Yutian Lei

Publication date: 10 October 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018236

zbMATH Keywords

positive solutionsHartree-Poisson equation

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Second-order elliptic systems (35J47)

Related Items (30)

Critical Stein-Weiss elliptic systems: symmetry, regularity and asymptotic properties of solutions ⋮ On elliptic equations with Stein-Weiss type convolution parts ⋮ Regularity, symmetry and asymptotic behaviour of solutions for some Stein-Weiss-type integral systems ⋮ Integrability of solutions for the integral system ⋮ Construction of infinitely many solutions for two-component Bose-Einstein condensates with nonlocal critical interaction ⋮ 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 ⋮ Classical solutions to a Hartree type system ⋮ Blow-up behavior of solutions to critical Hartree equations on bounded domain ⋮ Liouville theorems for a \(p\)-Laplace equation with Hartree type nonlinearity ⋮ Liouville theorem and qualitative properties of solutions for an integral system ⋮ On Liouville theorems of a Hartree–Poisson system ⋮ Liouville‐type theorem for finite Morse index solutions to the Choquard equation involving Δ_λ‐Laplacian ⋮ Stein-Weiss type inequality on the upper half space and its applications ⋮ Nondegeneracy of solutions for a critical Hartree equation ⋮ STABLE SOLUTIONS TO THE STATIC CHOQUARD EQUATION ⋮ Symmetry and nonexistence results for a fractional Choquard equation with weights ⋮ On a coupled Schrödinger system with Stein-Weiss type convolution part ⋮ Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system ⋮ Classification of nonnegative solutions to an equation involving the Laplacian of arbitrary order ⋮ High energy positive solutions for a coupled Hartree system with Hardy-Littlewood-Sobolev critical exponents ⋮ Symmetry and classification of solutions to an integral equation of the Choquard type ⋮ Liouville theorems for an integral equation of Choquard type ⋮ A sharp version of Phragmén-Lindelöf type theorem for the stationary Schrödinger equation ⋮ On classical solutions to the Hartree equation ⋮ Liouville theorem and classification of positive solutions for a fractional Choquard type equation ⋮ Qualitative properties and classification of solutions to elliptic equations with Stein-Weiss type convolution part ⋮ Construction of infinitely many solutions for a critical Choquard equation via local Pohožaev identities ⋮ Existence of concentrating solutions of the Hartree type Brezis-Nirenberg problem

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