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On the existence of periodic solutions for certain differential equations

Mehri, B ; Sharif University of Technology | 2005

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  1. Type of Document: Article
  2. DOI: 10.1016/j.cam.2004.04.011
  3. Publisher: 2005
  4. Abstract:
  5. Here we are concerned with the problem of the existence of periodic solution for certain second and third-order nonlinear differential equations. Our method here is to consider the problem as an eigenvalue problem and treat it by the topological degree theory. In particular we establish the conditions of the existence of periodic solution first for a simpler system which is homotopic to the original system and then generalize the obtained results for the focal system. The method employed here is applicable also for a system of nonlinear differential equations just with simple modifications. Finally, we present some specific examples numerically to show that the results are valid and realizable. © 2004 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Boundary conditions ; Eigenvalues and eigenfunctions ; Initial value problems ; Lyapunov methods ; Nonlinear equations ; Topology ; Periodic solution ; Schauder degree ; Topological degree thoery ; Differential equations
  8. Source: Journal of Computational and Applied Mathematics ; Volume 174, Issue 2 , 2005 , Pages 239-249 ; 03770427 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S037704270400192X