Liouville theorems for some nonlinear inequalities

DOI10.1134/S0081543808010070zbMath1233.35207OpenAlexW2071660239MaRDI QIDQ666549

Enzo Mitidieri, Lorenzo D'Ambrosio, Gabriella Caristi

Publication date: 8 March 2012

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543808010070

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Partial differential inequalities and systems of partial differential inequalities (35R45)

Related Items (26)

Representation formulae of solutions of second order elliptic inequalities ⋮ Liouville type theorems for systems of elliptic differential inequalities on Riemannian manifolds ⋮ A constructive approach to positive solutions of \(\delta_pu+f(u,u)\) on Riemannian manifolds ⋮ Absence of nonnegative solutions to the system of differential inequalities on manifolds ⋮ Solutions of multi-component fractional symmetric systems ⋮ Nonexistence results for systems of elliptic and parabolic differential inequalities in exterior domains of \(\mathbb{R}^n\) ⋮ On the existence of nonnegative solutions to semilinear differential inequality on Riemannian manifolds ⋮ Uniqueness of nonnegative solutions to elliptic differential inequalities on Finsler manifolds ⋮ Quasilinear Laplace equations and inequalities with fractional orders ⋮ Hardy-Littlewood-Sobolev systems and related Liouville theorems ⋮ Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings ⋮ Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds ⋮ Liouville type results for systems of equations involving fractional Laplacian in exterior domains ⋮ A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities ⋮ Liouville-type theorems for sign-changing solutions to nonlocal elliptic inequalities and systems with variable-exponent nonlinearities ⋮ Positive solutions for quasilinear elliptic inequalities and systems with nonlocal terms ⋮ Quasilinear elliptic inequalities with Hardy potential and nonlocal terms ⋮ On Nonnegative Solutions of the Inequality Δ u + u^σ ≤ 0 on Riemannian Manifolds ⋮ Representation formulae for nonhomogeneous differential operators and applications to PDEs ⋮ On nonexistence of positive solutions of quasi-linear inequality on Riemannian manifolds ⋮ On positive solutions of semi-linear elliptic inequalities on Riemannian manifolds ⋮ An elliptic system and the critical hyperbola ⋮ Absence of positive solutions to the system of differential inequalities on manifolds ⋮ Liouville type theorem for quasi-linear elliptic inequality \(\Delta_p u + u^\sigma \leqslant 0\) on Riemannian manifolds ⋮ \(L^p\)-Liouville theorems for invariant partial differential operators in \(\mathbb{R}^n\) ⋮ On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds

Cites Work

• Lectures on analysis on metric spaces
• Remark on some conformally invariant integral equations: the method of moving spheres
• Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.
• Representation formulae and inequalities for solutions of a class of second order partial differential equations
• Nonexistence results and estimates for some nonlinear elliptic problems
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