Symmetry breaking via Morse index for equations and systems of Hénon-Schrödinger type

Zhenluo Lou, Tobias Weth, Zhitao Zhang

We consider the Dirichlet problem for the Schrödinger-Hénon system $$-\Delta u+{\mu }_{1}u=|x{|}^{\alpha }{\partial }_{u}F(u,v),-\Delta v+{\mu }_{2}v=|x{|}^{\alpha }{\partial }_{v}F(u,v)$$ in the unit ball $Ω\…