Existence of solutions on the critical hyperbola for a pure Lane-Emden system with Neumann boundary conditions

Angela Pistoia, Delia Schiera, Hugo Tavares

We study the following Lane-Emden system \[ -Δu=|v|^{q-1}v \quad \text{ in } Ω, \qquad -Δv=|u|^{p-1}u \quad \text{ in } Ω, \qquad u_ν=v_ν=0 \quad \text{ on } \partial Ω, \] with $Ω…