Existence of periodic solutions of ordinary differential equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Teixeira, Joao¹  Borges, Maria Joao¹ 

[1] Univ Tecn Lisboa, Inst Super Tecn, Dept Matemat, CAMGSD, Lisbon, Portugal

关键词: Ordinary differential equations;    Periodic solutions;    Euler iterates;    Brouwer fixed point theorem;    Forced oscillations;    Solow equation;    Forced nonlinear dissipative pendulum;   

DOI  :  10.1016/j.jmaa.2011.06.048

来源: Elsevier

【 摘 要 】

We prove the existence of a periodic solution, y is an element of C-1 (R. R-l), of a first-order differential equation (y) over dot = f (t, y), where f is periodic with respect to t and admits a star-shaped compact set that is invariant under the Euler iterates of the equation with sufficiently small time-step. As in Peano's Theorem for the Cauchy problem, the only required regularity condition on f is continuity. We present two nontrivial examples that illustrate the usefulness of this theorem in applications related to forced oscillations. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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