Year 2020

• On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems

  Publication

  • J. Ciesielski
  • J. Janczewska
  • N. Waterstraat

  - Journal of Dynamics and Differential Equations - Year 2020

  We show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...

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Year 2013

• A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions

  Publication

  • G. Graff
  • A. Ruiz-Herrera

  - Journal of Dynamics and Differential Equations - Year 2013

  In this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...

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Year 2011

• Local fixed point indices of iterations of planar maps

  Publication

  • G. Graff
  • P. Nowak-Przygodzki
  • F. Ruiz Del Portal

  - Journal of Dynamics and Differential Equations - Year 2011

  W artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.

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