On a critical Hamiltonian system with Neumann boundary conditions

2024/06/30 by Pistoia, Angela, Schiera, Delia
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.00794

Abstract

We consider the Hamiltonian system with Neumann boundary conditions: -Δu + μu=v^q , -Δv+ μv=u^p in Ω, u, v gt;0 in Ω, ∂_νu= ∂_νv=0 on ∂ Ω, where μ>0 is a parameter and Ω is a smooth bounded domain in \mathbb R^N . When (p, q) approaches from below the critical hyperbola N/(p+1) + N/(q+1)=N-2, we build a solution which blows-up at a boundary point where the mean curvature achieves its minimum and negative value.

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