Asymptotic equivalence of differential equations and asymptotically almost periodic solutions

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2007-09-15

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Akhmet, Marat
Zafer, A.

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In this paper we use Rab's lemma [M. Rab, Uber lineare perturbationen eines systems von linearen differentialgleichungen, Czechoslovak Math. J. 83 (1958) 222-229; M. Rab, Note sur les formules asymptotiques pour les solutions d'un systeme d'equations differentielles lineaires, Czechoslovak Math. J. 91 (1966) 127-129] to obtain new sufficient conditions for the asymptotic equivalence of linear and quasilinear systems of ordinary differential equations. Yakubovich's result [V.V. Nemytskii, VX Stepanov, Qualitative Theory of Differential Equations, Princeton University Press, Princeton, New Jersey, 1966; V.A. Yakubovich, On the asymptotic behavior of systems of differential equations, Mat. Sb. 28 (1951) 217-240] on the asymptotic equivalence of a linear and a quasilinear system is developed. On the basis of the equivalence, the existence of asymptotically almost periodic solutions of the systems is investigated. The definitions of biasymptotic equivalence for the equations and biasymptotically almost periodic solutions are introduced. Theorems on the sufficient conditions for the systems to be biasymptotically equivalent and for the existence of biasymptotically almost periodic solutions are obtained. Appropriate examples are constructed.

Subject Keywords

Applied Mathematics, Analysis

URI

https://hdl.handle.net/11511/42935

Journal

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

DOI

https://doi.org/10.1016/j.na.2006.07.045

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet and A. Zafer, “Asymptotic equivalence of differential equations and asymptotically almost periodic solutions,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 1870–1877, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42935.