Asymptotic integration of linear differential-algebraic equations

This paper is concerned with the asymptotic behavior of solutions of linear differential-algebraic equations (DAEs) under small nonlinear perturbations. Some results on the asymptotic behavior of solutions which are well known for ordinary differential equations are extended to DAEs. The main tools are the projector-based decoupling and the contractive mapping principle. Under certain assumptions on the linear part and the nonlinear term, asymptotic behavior of solutions are characterized. As the main result, a Perron type theorem that establishes the exponential growth rate of solutions is formulated.

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Asymptotic behaviour of solutions of quasilinear differential-algebraic equations

Linh

Nga

Nguyen

2022

Electron. J. Qual. Theory Differ. Equ.

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On the preservation of Lyapunov exponents of integrally separated systems of differential equations under small nonlinear perturbations

Vu,

Nga

2024

Electron. J. Qual. Theory Differ. Equ.

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This paper addresses the Lyapunov exponents of non-vanishing solutions to quasi-linear time-varying systems of differential equations. The linear part is not required to be regular but it is assumed to be integrally separated, which ensures that the associated Lyapunov exponents are distinct and stable. The nonlinear perturbations are assumed to be small in a certain sense, though less restrictive than the condition in Barreira and Valls’ paper, J. Differential Equations 258(2015), 339–361. The main result is a Perron-type theorem for upper and lower Lyapunov exponents, offering an alternative to Barreira and Valls’ result. In addition, an analogous result holds for Bohl exponents.

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Asymptotic integration of linear differential-algebraic equations

Cited by 2 publications

References 19 publications

Asymptotic behaviour of solutions of quasilinear differential-algebraic equations

Asymptotic behaviour of solutions of quasilinear differential-algebraic equations

On the preservation of Lyapunov exponents of integrally separated systems of differential equations under small nonlinear perturbations

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