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.
On the Poincaré-Hopf theorem for functionals defined on Banach Spaces / Cingolani, Silvia; Degiovanni, Marco. - In: ADVANCED NONLINEAR STUDIES. - ISSN 1536-1365. - STAMPA. - 9:4(2009), pp. 679-699. [10.1515/ans-2009-0406]
On the Poincaré-Hopf theorem for functionals defined on Banach Spaces
Silvia Cingolani;
2009
Abstract
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.File in questo prodotto:
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