Let X be a reflexive Banach space and f : X → ℝ a Gateaux differentiable function with f' demicontinuous and locally of class (S) + . We prove that each isolated critical point of f has critical groups of finite type and that the Poincaré- Hopf formula holds. We also show that quasilinear elliptic equations at critical growth are covered by this result.
|Titolo:||On the Poincaré-Hopf theorem for functionals defined on Banach Spaces|
|Data di pubblicazione:||2009|
|Appare nelle tipologie:||1.1 Articolo in rivista|