Asymptotic behavior of positive solutions to the Lane-Emden system in dimension two

2022/04/07 by Zhijie, Chen, Houwang Li, Wenming Zou +2 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.03422

openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the Lane-Emden system \beginaligned amp;-Δu=v^p, ugt;0,\quadin~Ω, amp;-Δv=u^q, vgt;0,\quadin~Ω, amp;u=v=0,\quadon~∂Ω, \endaligned where Ω is a smooth bounded domain in ℝ^N with N≥ 2 and q≥ p>0. The asymptotic behavior of \it least energy solutions of this system was studied for N≥ 3. However, the case N=2 is different and remains completely open. In this paper, we study the case N=2 with q=p+θ_p and sup_pθ_p

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