Infinitely many solutions to perturbed elliptic equations

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