On finite Morse index solutions to the quadharmonic Lane-Emden equation

2016/09/05 by Senping Luo, Juncheng Wei, Luo, Senping +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1609.01269

openalex publication_date 2016/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we compute the Joseph-Lundgren exponent for the quadharmonic Lane-Emden equation, derive a monotonicity formula and classify the finite Morse index solution to the following quadharmonic Lane-Emden equation: \noindent Δ⁴ u=|u|^p-1u \hboxin \Rⁿ. As a byproduct, we also get a monotonicity formula for the quadharmonic maps Δ⁴ u=0.

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

Related

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• On the fractional Lane-Emden equation
• On finite Morse index solutions of higher order fractional Lane-Emden equations
• A Morse index formula for radial solutions of Lane-Emden problems
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