Liouville type theorems for integral equations and integral systems

DOI10.1007/s00526-011-0474-zzbMath1262.45004OpenAlexW2068013636MaRDI QIDQ1937824

Xiaohui Yu

Publication date: 1 February 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-011-0474-z

zbMATH Keywords

positive solutionmethod of moving planesLiouville type theoremssingular nonlinear integral equations

Mathematics Subject Classification ID

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

Related Items (39)

Critical Stein-Weiss elliptic systems: symmetry, regularity and asymptotic properties of solutions ⋮ Symmetry of positive solutions of fractional Laplacian equation and system with Hardy-Sobolev exponent on the unit ball ⋮ Liouville theorem for Choquard equation with finite Morse indices ⋮ Liouville theorems for an integral system with Poisson kernel on the upper half space ⋮ On critical systems involving fractional Laplacian ⋮ Liouville type theorems for singular integral equations and integral systems ⋮ Radial symmetry results for fractional Laplacian systems ⋮ Classification of solutions to higher fractional order systems ⋮ Liouville type theorem of integral equation with anisotropic structure ⋮ Direct method of moving planes for logarithmic Laplacian system in bounded domains ⋮ Liouville type theorem for some nonlocal elliptic equations ⋮ On the ground state solution for a critical fractional Laplacian equation ⋮ Property of solutions for elliptic equation involving the higher-order fractional Laplacian in \(\mathbb{R}^n_+\) ⋮ Solutions of fractional Laplacian equations and their Morse indices ⋮ Liouville type theorem for nonlinear elliptic equation involving Grushin operators ⋮ Classification of solutions for some mixed order elliptic system ⋮ Liouville theorems for Hénon type Choquard equation ⋮ Liouville type theorems for Hartree and Hartree-Fock equations ⋮ Symmetry of solutions for a fractional system ⋮ Symmetry for an integral system with general nonlinearity ⋮ Liouville type theorem for nonlinear elliptic equation with general nonlinearity ⋮ On the integral systems with negative exponents ⋮ Liouville theorem for an integral system on the upper half space ⋮ Wolff type potential estimates and application to nonlinear equations with negative exponents ⋮ Symmetry of positive solutions for Hartree type nonlocal Lane-Emden system ⋮ Liouville type theorems for nonlinear elliptic equations on extended Grushin manifolds ⋮ Liouville type theorems for general integral system with negative exponents ⋮ Liouville type theorems for two mixed boundary value problems with general nonlinearities ⋮ Liouville type results for systems of equations involving fractional Laplacian in exterior domains ⋮ Necessary conditions for existence results of some integral system ⋮ A Liouville theorem for a class of fractional systems in \(\mathbb{R}_+^n\) ⋮ Liouville-type theorem for higher-order Hardy-Hénon system ⋮ Positive least energy solutions for \(k\)-coupled critical systems involving fractional Laplacian ⋮ Multi-spike positive solutions for nonlinear fractional Schrödinger equations ⋮ Sliding methods for a class of generalized fractional Laplacian equations ⋮ On strongly indefinite systems involving the fractional Laplacian ⋮ Liouville theorems for fractional Hénon equation and system on \(\mathbb{R}^n\) ⋮ Sharp criteria of Liouville type for some nonlinear systems ⋮ Infinitely many sign-changing solutions of a critical fractional equation

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