Opis

• Tytuł:
  Existence, localization and stability of limit-periodic solutions to differential equations involving cubic nonlinearities
• Twórca:
  Andres, Jan;
  Pennequin, Denis
• Opis:
  We will prove, besides other things like localization and (in)stability, that the differential equations $x'+x^3-\lambda x=\varepsilon r(t)$, $\lambda> 0$, and $x''+x^3-x=\varepsilon r(t)$, where $r\colon\mathbb{R}\to\mathbb{R}$ are uniformly limit-periodic functions, possess for sufficiently small values of $\varepsilon > 0$ uniformly limit-periodic solutions, provided $r$ in the first-order equation is strictly positive. As far as we know, these are the first nontrivial effective criteria, obtained for limit-periodic solutions of nonlinear differential equations, in the lack of global lipschitzianity restrictions. A simple illustrative example is also indicated for difference equations.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Data:
  2019.07.13
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2B (December 2019); 887 - 906;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031/17999 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031/18000
• Temat i słowa kluczowe:
  Limit-periodic solutions;
  differential equations;
  cubic nonlinearity;
  existence of solutions;
  localization;
  (in)stability;
  essentiality;
  34C15;
  34C27;
  34K14
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.031
• Dostawca danych:
  Akademicka Platforma Czasopism
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