Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems

DOI10.1016/j.jde.2009.09.012zbMath1185.35066arXiv0906.2345OpenAlexW1974171839MaRDI QIDQ960831

Tobias Weth, Wolfgang Reichel

Publication date: 29 March 2010

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.2345

zbMATH Keywords

existencetopological degreeLiouville theoremshigher order equation

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) A priori estimates in context of PDEs (35B45) Variational methods for higher-order elliptic equations (35J35) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (19)

Liouville type theorem for critical order Hénon-Lane-Emden type equations on a half space and its applications ⋮ On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Classification theorems for solutions of higher order boundary conformally invariant problems. I. ⋮ Liouville type theorem to an integral system in the half-space ⋮ Liouville-type theorems for higher-order Lane–Emden system in exterior domains ⋮ Liouville type theorems for elliptic equations with Dirichlet conditions in exterior domains ⋮ A Liouville type theorem for poly-harmonic Dirichlet problems in a half space ⋮ Liouville type theorems for poly-harmonic Dirichlet problems of Hénon-Hardy type equations on a half space or a ball ⋮ Liouville type theorem for higher order Hénon equations on a half space ⋮ Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth ⋮ An elliptic problem involving large advection ⋮ Pointwise bounds and blow-up for nonlinear polyharmonic inequalities ⋮ Positivity for fourth-order semilinear problems related to the Kirchhoff-love functional ⋮ Isolated singularities of polyharmonic inequalities ⋮ Liouville-type theorems and decay estimates for solutions to higher order elliptic equations ⋮ Liouville-type theorems for integral and PDE systems with critical exponents in a half space ⋮ Nonexistence of positive solutions to \(n\)-th order equations in \(\mathbb{R}^n\) ⋮ Nonexistence of Positive Supersolutions of Nonlinear Biharmonic Equations without the Maximum Principle ⋮ Liouville type theorem for higher-order elliptic system with Navier boundary condition

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