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 S.
;
2009-01-01

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/206228
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