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

Marco Degiovanni, Silvia Cingolani

Research output: Contribution to journalArticlepeer-review

12 Citations (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.
Original languageEnglish
Pages (from-to)679-699
Number of pages21
JournalAdvanced Nonlinear Studies
Volume9
Publication statusPublished - 2009

Keywords

  • Critical point theory
  • Equazioni differenziali
  • Teoria dei punti critici

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