On least energy solutions to a pure Neumann Lane-Emden system: convergence, symmetry breaking, and multiplicity

Alberto Saldaña, Delia Schiera, Hugo Tavares

We consider the following Lane-Emden system with Neumann boundary conditions \[ -Δu= |v|^{q-1}v \text{ in } Ω,\qquad -Δv= |u|^{p-1}u \text{ in } Ω,\qquad \partial_νu=\partial_νv=0…