Liouville theorems for a class of fourth order elliptic equations

DOI10.1017/S0308210500012063zbMath0452.35023OpenAlexW2112672622MaRDI QIDQ3898852

Philip W. Schaefer, Vinod B. Goyal

Publication date: 1980

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500012063

zbMATH Keywords

maximum principlesfunctionalsgradient estimatesLiouville type theoremssubharmonicityfourth order equations

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Higher-order elliptic equations (35J30)

Related Items (6)

Liouville-type results for fourth order elliptic equations ⋮ Liouville's theorem for the drifting Laplacian ⋮ Liouville-type and uniqueness results for a class of sixth-order elliptic equations ⋮ Liouville theorems for linear elliptic systems ⋮ Liouville theorems for elliptic systems and nonlinear equations of fourth order ⋮ Liouville-type and uniqueness results for a class of elliptic equations

Cites Work

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• Ganze Lösungen der Differentialgleichung \(\Delta^p u = f(u)\)
• Liouville theorems and gradient bounds for quasilinear elliptic systems
• A differential inequality
• On the inequality \(\Delta u\geq f(u, |grad u|)\)
• On solutions of δu=f(u)
• On the Nonexistence of Entire Solutions to Nonlinear Second Order Elliptic Equations
• On Liouville’s Theorem for Biharmonic Functions
• Entire Solutions of Nonlinear Poisson Equations
• A Note on Unrestricted Solutions of the Differential Equation Δu =f (u )

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