On a critical Hamiltonian system with Neumann boundary conditions - Pistoia, Angela; Schiera, Delia (Topological Methods in Nonlinear Analysis, 2025)
We consider the Hamiltonian system with Neumann boundary conditions: \[ cases -Δ u + μ u=v^q & in Ω, -Δ v+ μ v=u^p & in Ω, u, v > 0 & in Ω, _ u u= _ u v=0 & on Ω, cases \] where μ > 0 is a parameter and Ω is a smooth bounded domain in 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.