On the Poincaré-Hopf theorem for functionals defined on Banach spaces

Silvia Cingolani; Marco Degiovanni

doi:10.1515/ans-2009-0406

On the Poincaré-Hopf theorem for functionals defined on Banach spaces

Silvia Cingolani^*, Marco Degiovanni

^*Autore corrispondente per questo lavoro

Facoltà di Scienze Matematiche, Fisiche e Naturali

Polytechnic University of Bari

Risultato della ricerca: Contributo in rivista › Articolo › peer review

12 Citazioni (Scopus)

Abstract

Let X be a reflexive Banach space and f a Gâteaux 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.

Lingua originale	Inglese
pagine (da-a)	679-699
Numero di pagine	21
Rivista	Advanced Nonlinear Studies
Volume	9
Numero di pubblicazione	4
DOI	https://doi.org/10.1515/ans-2009-0406
Stato di pubblicazione	Pubblicato - 2009

All Science Journal Classification (ASJC) codes

Fisica Statistica e Non Lineare
Matematica generale

Keywords

Critical point theory
Equazioni differenziali
Teoria dei punti critici

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10.1515/ans-2009-0406

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AB - Let X be a reflexive Banach space and f a Gâteaux 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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KW - Equazioni differenziali

KW - Teoria dei punti critici

KW - Critical point theory

KW - Equazioni differenziali

KW - Teoria dei punti critici

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On the Poincaré-Hopf theorem for functionals defined on Banach spaces

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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