Asymptotic decay of solutions to an essentially nonlinear system with two-frequency resonances. Issue 11 (1st November 2016)

• Record Type: Journal Article
• Authors: Grushkovskaya, Victoria
• Is Part Of: Applicable analysis. Volume 95:Issue 11(2016)
• Page Start: 2501
• Page End: 2516
• Publication Date: 2016-11-01
• Subjects: Asymptotic estimate -- critical case -- Lyapunov function -- resonance -- stability; 34D05 -- 34D20 -- 70E55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1094798
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper is focused on the analysis of the asymptotic behavior of solutions for a nonlinear system with pairs of purely imaginary roots under the presence of two-frequency resonances of the fourth order. The main purpose of the paper is to estimate the norm of solutions, provided that the trivial solution is asymptotically stable regardless of forms higher than the third order. For this study, asymptotic stability conditions are presented and a Lyapunov function is constructed. These results are applied for estimating the decay rate of oscillations of a spring-pendulum system with partial dissipation.