Infinitely many solutions to perturbed elliptic equations

A new version of perturbation theory is developed which produces infinitely many sign-changing critical points for uneven functionals. The abstract result is applied to the following elliptic equations with a Hardy potential and a perturbation from symmetry:-Δu-μu|x|2=f(x,u)+p(x,u) in Ω,u=0 on ∂Ωand-Δu=|u|q-2|x|su+p(x,u) in Ω,u=0 on ∂Ω,where 0