Opis

• Tytuł:
  Massera's theorem for quasi-periodic differential equations
• Twórca:
  Ortega, Rafael;
  Tarallo, Massimo
• Opis:
  For a scalar, first order ordinary differential equation which depends periodically on time, Massera's Theorem says that the existence of a bounded solution implies the existence of a periodic solution. Though the statement is false when periodicity is replaced by quasi-periodicity, solutions with some kind of recurrence are anyway expected when the equation is quasi-periodic in time. Indeed we first prove that the existence of a bounded solution implies the existence of a solution which is quasi-periodic in a weak sense. The partial differential equation, having our original equation as its equation of characteristics, plays a key role in the introduction of this notion of weak quasi-periodicity. Then we compare our approach with others already known in the literature. Finally, we give an explicit example of the weak case, and an extension to higher dimension for a special class of equations.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Data:
  2002.03.01
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 19, No 1 (March 2002); 39 - 61;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.003/9658
• Temat i słowa kluczowe:
  Bounded;
  recurrent and quasi-periodic solutions;
  partial differential equations on the torus;
  Primary 34C27;
  37B55;
  Secondary 37B20;
  35F30
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2002.003
• Dostawca danych:
  Akademicka Platforma Czasopism
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