the Hénon equationthe Hénon equationThe Henon equation and its associated energy functional can be written as{-Δu=|x|r|u|q-1u,x∈Ωu=0,x∈∂Ω,J(u)=∫Ω[12|∇u|2-1q+1|x|r|u|q+1]𝑑xwhere u∈H01(Ω), Ω⊂ℝN(N≥2)is an open bounded domain, r≥0 and 1<q≤N+2N-2.