On the triharmonic Lane-Emden equation

2016/07/16 by Senping Luo, Juncheng Wei, Luo, Senping +3 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.1607.04719

51 pages; comments are welcome

arxiv created 2016/07/16 · openalex publication_date 2016/07/16 · arxiv updated 2016/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a monotonicity formula and classify finite Morse index solutions (positive or sign-changing, radial or not) to the following triharmonic Lane-Emden equation: (-Δ)³ u=|u|^p-1u \hbox in ℝⁿ, where p is below the Joseph-Lundgren exponent. As a byproduct we also obtain a new monotonicity formula for the triharmonic maps.

Citations

• Quasilinear Dirichlet problems driven by positive sources
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

Cited by

• Classification of the stable solution to the fractional 2<s<3 Lane-Emden equation
• On finite Morse index solutions to the quadharmonic Lane-Emden equation

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• A Morse index formula for radial solutions of Lane-Emden problems
• Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains