## Abstract and Applied Analysis

### Nontrivial Periodic Solutions of an $n$-Dimensional Differential System and Its Application

F. B. Gao

#### Abstract

Two criteria are constructed to guarantee the existence of periodic solutions for a second-order $n$-dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 140173, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393444299

Digital Object Identifier
doi:10.1155/2013/140173

Mathematical Reviews number (MathSciNet)
MR3102659

Zentralblatt MATH identifier
06306057

#### Citation

Gao, F. B. Nontrivial Periodic Solutions of an $n$ -Dimensional Differential System and Its Application. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 140173, 9 pages. doi:10.1155/2013/140173. https://projecteuclid.org/euclid.aaa/1393444299

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