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On the existence of periodic solutions for the quasi-linear third-order differential equation

Mehri, B ; Sharif University of Technology | 2001

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  1. Type of Document: Article
  2. DOI: 10.1006/jmaa.2001.7486
  3. Publisher: 2001
  4. Abstract:
  5. In this paper we consider the nonlinear third-order quasi-linear differential equationx‴+k2x′=εfx,x′,x″and obtain some simple conditions for the existence of a periodic solution for it. In so doing we use the implicit function theorem to prove a theorem about the existence of periodic solutions and consider one example to show the realizability of the conditions. The validity of the conditions for the parameter-free problemx‴+k2x′=fx,x′,x″also is considered. © 2001 Academic Press
  6. Keywords:
  7. Homotopy invariance ; Nonlinear equations ; Periodic solutions ; Topological degree
  8. Source: Journal of Mathematical Analysis and Applications ; Volume 261, Issue 1 , 2001 , Pages 159-167 ; 0022247X (ISSN)
  9. URL: https://linkinghub.elsevier.com/retrieve/pii/S0022247X01974864