Asymptotic behavior of solutions of elliptic equations. II: Analogues of Liouville's theorem for solutions of inequalities on \(R^ n\), \(n\geq 3\)

DOI10.1007/BF02803332zbMath0477.35040OpenAlexW2050886679MaRDI QIDQ1160816

Leon Karp

Publication date: 1981

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02803332

zbMATH Keywords

quasilinear elliptic inequalitiesLiouville-type theoremsbounded nonconstant solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Partial differential inequalities and systems of partial differential inequalities (35R45) Nonlinear elliptic equations (35J60) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (7)

Rigidity results for stable solutions of symmetric systems ⋮ Solutions of multi-component fractional symmetric systems ⋮ Subharmonic functions on real and complex manifolds ⋮ Asymptotic behavior of solutions of elliptic equations. I: Liouville-type theorems for linear and nonlinear equations on \(R^ n\). ⋮ New Liouville theorems for linear second order degenerate elliptic equations in divergence form. ⋮ A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities ⋮ Symmetry Results for Fractional Elliptic Systems and Related Problems

Cites Work

• Lower bounds at infinity for solutions of differential equations with constant coefficients
• On isolated singularities of solutions of second order elliptic differential equations
• Liouville theorems for nonlinear elliptic equations and systems
• Subharmonic functions on real and complex manifolds
• Asymptotic behavior of solutions of elliptic equations. I: Liouville-type theorems for linear and nonlinear equations on \(R^ n\).
• Asymptotic properties of solutions of differential equations with simple characteristics
• Local behavior of solutions of quasi-linear equations
• Isolated singularities of solutions of quasi-linear equations
• Entire solutions of partial differential equations with constant coefficients
• Decay at infinity of solutions to higher order partial differential equations: removal of the curvature assumption
• Bounded entire solutions of elliptic equations
• A Harnack inequality for nonlinear equations
• Decay at Infinity of Solutions to Partial Differential Equations with Constant Coefficients
• On harnack type inequalities and their application to quasilinear elliptic equations
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