On Existence of Periodic Solutions for Certain Nonlinear Higher Order Autonomous Ordinary Differential Equations

Journal Article · Wed Sep 17 00:00:00 EDT 2008 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2997322· OSTI ID:21251377

Bayat, M; Khatami, Z; Mehri, B ^[1]

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1. Department of Mathematics, Institute for Advanced Studies in Basic Sciences 45195-1159, Zanjan (Iran, Islamic Republic of)

In this paper, we study the existence of periodic solutions for autonomous nonlinear ordinary differential equations of order n. Our method is based on the evaluation of Brouwer's degree theory and making use of the homotopy invariance property of the topological degree and also suitable norm inequalities. For this, we prove two lemmas about the second and third order ODE systems and then present two theorems about the sufficient conditions for the existence of periodic solutions for the even and odd n-order ODE respectively.

• OSTI ID: 21251377
• Journal Information: AIP Conference Proceedings, Vol. 1046, Issue 1; Conference: ICNAAM-2007: International conference on numerical analysis and applied mathematics 2007; ICCMSE-2007: International conference on computational methods in sciences and engineering 2007, Corfu (Greece), 16-20 Sep 2007; 25-30 Sep 2007; Other Information: DOI: 10.1063/1.2997322; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EVALUATION
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
PERIODICITY
TOPOLOGY