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Stability Behavior of the Zero Solution for Nonlinear Damped Vectorial Second Order Differential Equation
Department of Mathematics, Faculty of Science, Minufiya University, Shebeen El-koom, Egypt
Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El-Sheikh University, Kafr El-Sheikh, Egypt
- 1 Department of Mathematics, Faculty of Science, Minufiya University, Shebeen El-koom, Egypt
- 2 Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El-Sheikh University, Kafr El-Sheikh, Egypt
International Journal of Modern Nonlinear Theory and Application·Volume 01 (2012)·Pages 125–129·Published 31 December 2012·DOI10.4236/ijmnta.2012.14019
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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.
KeywordsZero SolutionDamped OscillatorUniformly StableAsymptotically Stable
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