Rok 2019

• Bernstein-type theorem for ϕ-Laplacian

  Publikacja

  • J. Maksymiuk
  • J. Ciesielski
  • M. Starostka

  - Fixed Point Theory and Applications - Rok 2019

  In this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...

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• The Maslov index and the spectral flow—revisited

  Publikacja

  • M. Izydorek
  • J. Janczewska
  • N. Waterstraat

  - Fixed Point Theory and Applications - Rok 2019

  We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space. Finally, we obtain from Cappell,...

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Rok 2008

• Some remarks on the Euler ring U(G)

  Publikacja

  • K. Gęba
  • S. Rybicki

  - Fixed Point Theory and Applications - Rok 2008

  Niech G będzie zwartą grupą Liego i niech U(G) oznacza pierściń Eulera G skonstruoawany przez tom Diecka w [5,6]. Główny wynikpracy (Twierdzenie 4.1) opisuje homomorfizm pierścienia U(SO(3)) w pierścień U(SO(2))indukowany przez włożenie grupy SO(2) w grupę SO(3).