Liouville type theorems for singular integral equations and integral systems

DOI10.3934/cpaa.2016017zbMath1352.45015OpenAlexW2469839174MaRDI QIDQ324050

Xiaohui Yu

Publication date: 10 October 2016

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2016017

zbMATH Keywords

integral equationpositive solutionsHardy-Littlewood-Sobolev inequalityLiouville-type theoremmoving planesHardy termintegral systems

Mathematics Subject Classification ID

Systems of nonlinear integral equations (45G15) Singular nonlinear integral equations (45G05) Positive solutions of integral equations (45M20)

Related Items

Liouville-type theorem for Kirchhoff equations involving Grushin operators, Liouville type theorem for Hartree-Fock equation on half space, Liouville type theorem for some nonlocal elliptic equations, On the ground state solution for a critical fractional Laplacian equation, Solutions of fractional Laplacian equations and their Morse indices, Liouville type theorems for Hartree and Hartree-Fock equations, Liouville type theorem for nonlinear elliptic equation with general nonlinearity, Liouville type theorems for nonlinear elliptic equations on extended Grushin manifolds, Liouville type theorems for two mixed boundary value problems with general nonlinearities, Method of scaling spheres for integral and polyharmonic systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Liouville type theorem for poly-harmonic Dirichlet problems in a half space
• Regularity of solutions for an integral system of Wolff type
• Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
• An integral system and the Lane-Emden conjecture
• Classification of positive solitary solutions of the nonlinear Choquard equation
• Classification of positive solutions for nonlinear differential and integral systems with critical exponents
• An integral equation in conformal geometry
• The proof of the Lane-Emden conjecture in four space dimensions
• Symmetry and related properties via the maximum principle
• Classification of solutions of some nonlinear elliptic equations
• Remark on some conformally invariant integral equations: the method of moving spheres
• Some nonexistence results for positive solutions of elliptic equations in unbounded domains.
• Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions
• On positive entire solutions to a class of equations with a singular coefficient and critical exponent
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Non-existence of positive solutions of Lane-Emden systems
• Liouville type theorems for integral equations and integral systems
• Radial symmetry of solutions for some integral systems of Wolff type
• Radial symmetry and uniqueness for positive solutions of a Schrödinger type system
• A Liouville type theorem for an integral system
• Radial symmetry and monotonicity for an integral equation
• Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems
• Symmetry of solutions to some systems of integral equations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Uniqueness of Positive Bound States to Schrödinger Systems with Critical Exponents
• A priori bounds for positive solutions of nonlinear elliptic equations
• Non—existence of positive solutions to semilinear elliptic equations on r” or r” through the method of moving planes
• Classification of Solutions for a System of Integral Equations
• Liouville Type Theorems for Positive Solutions of Elliptic System in ℝ^N
• Classification of solutions for an integral equation