Stability Behavior of the Zero Solution for Nonlinear Damped Vectorial Second Order Differential Equation

Mohamed A. Ramadan, Samah M. El-Kholy

Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El-Sheikh University, Kafr El-Sheikh, Egypt.
Department of Mathematics, Faculty of Science, Minufiya University, Shebeen El-koom, Egypt.

DOI: 10.4236/ijmnta.2012.14019                

Abstract

In this paper, a theoretical treatment of the stability behavior of the zero solution of nonlinear damped oscillator in the vectorial case is investigated. We study the sufficient conditions for the boundedness of solution of the nonlinear damped vectorial oscillator and the conditions for the stability of the zero solution to be uniformly stable as well as asymptotically stable.

Keywords

Zero Solution; Damped Oscillator; Uniformly Stable; Asymptotically Stable

Conflicts of Interest

The authors declare no conflicts of interest.

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