Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle

DOI10.1080/03605302.2015.1008364zbMath1456.35239arXiv1407.4506OpenAlexW2111215635MaRDI QIDQ5256315

Steven D. Taliaferro, Marius Ghergu

Publication date: 22 June 2015

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.4506

zbMATH Keywords

new representation formula, a priori pointwise bound for nonnegative solutions

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Partial differential inequalities and systems of partial differential inequalities (35R45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Higher-order elliptic equations (35J30) Semilinear elliptic equations (35J61) Positive solutions to PDEs (35B09)

Related Items (4)

Local behavior of solutions to a biharmonic equation with isolated singularity ⋮ Nonexistence of solutions of a semilinear biharmonic equation with singular potential ⋮ Least energy solutions for indefinite biharmonic problems via modified Nehari–Pankov manifold ⋮ Unnamed Item

Cites Work

• Isolated singularities of polyharmonic inequalities
• A note on nonlinear biharmonic equations with negative exponents
• Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems
• A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
• Representation formulae for solutions to some classes of higher order systems and related Liouville theorems
• Removable singularity of the polyharmonic equation
• Classification of solutions of higher order conformally invariant equations
• Isolated singularities of super-polyharmonic functions
• Nonlinear biharmonic equations with negative exponents
• Pointwise bounds and blow-up for nonlinear polyharmonic inequalities
• Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle
• Liouville-type theorems for polyharmonic equations in $\mathbb{R}^N$ and in $\mathbb{R}^N_+$
• Uniqueness theorem for the entire positive solutions of biharmonic equations in Rⁿ

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