The Solution of Nonlinear Systems of Equations by Second Order Systems of O.D.E. and Linearly Implicit A-Stable Techniques

1982 ◽  
Vol 19 (4) ◽  
pp. 800-815 ◽  
Author(s):  
Francesco Zirilli
Keyword(s):  
Nonlinear Systems ◽  
Second Order ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Second Order Systems

scholarly journals On the problem of stability of a motion of essentially nonlinear systems

2021 ◽  
pp. 3-12
Author(s):  
A.A. Martynyuk ◽  
V.O. Chernienko
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Systems Of Equations ◽  
Affine Systems ◽  
The Stability ◽  
Second Order Systems

This article discusses essentially nonlinear systems. Following the approach of applying the pseudolinear inequalitiesdeveloped in a number of works, new estimates for the variation of Lyapunov functions along solutionsof the considered systems of equations are obtained. Based on these estimates, we obtain sufficient conditionsfor the equiboundedness of solutions of second-order systems and sufficient conditions for the stability of anessentially nonlinear system under large initial perturbations. Conditions for the stability of affine systems arealso obtained.

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