New type of solutions for the critical Lane-Emden system

2024/01/18 by Wenjing Chen, Chen, Wenjing, Xiaomeng Huang +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2401.09713

openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the critical Lane-Emden system \begincases -Δu=K₁(y)v^p, y∈ ℝ^N,amp;
-Δv=K₂(y)u^q, y∈ ℝ^N,amp;
u,vgt;0, \endcases where N≥ 5, p,q∈ (1,∞) with (1)/(p+1)+(1)/(q+1)=(N-2)/(N), K₁(y) and K₂(y) are positive radial potentials. Under suitable conditions on K₁(y) and K₂(y), we construct a new family of solutions to this system, which are centred at points lying on the top and the bottom circles of a cylinder.

Related

• A new critical curve for the Lane-Emden system
• Radially symmetric solutions to a Lane-Emden type system
• Entire nodal solutions to the critical Lane-Emden system
• Coron's problem for the critical Lane-Emden system
• Asymptotically homogeneous solutions of the supercritical Lane-Emden system