The Ψ–Asymptotic Equivalence of the Lyapunov Matrix Differential Equations with Integral Term as Right Side and Modified Argument

Diamandescu, Aurel

doi:10.2478/awutm-2022-0018

Abstract

Using the notion of strict h-contraction, existence results for Ψ-asymptotic equivalence of two pairs of (Lyapunov) matrix differential equations with integral term as right side and modified argument are given.

References

[1] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill Company, Inc. New York 1960.
Search in Google Scholar Back to article
[2] F. Brauer, J. S. W. Wong, On asymptotic behavior of perturbed linear systems, J. Differential Equations 6 (1969), 142–153.10.1016/0022-0396(69)90122-3
Search in Google Scholar Back to article
[3] F. Brauer, J. S. W. Wong, On asymptotic relationships between solutions of two systems of ordinary differential equations, J. Differential Equations 6 (1969), 527–543.10.1016/0022-0396(69)90008-4
Search in Google Scholar Back to article
[4] W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, D. C. Heath and Company, Boston, 1965.
Search in Google Scholar Back to article
[5] A. Diamandescu, On the Ψ-asymptotic equivalence of the Ψ - bounded solutions of two Lyapunov matrix differential equations, ITM Web of Conferences 34 (2020), 03006.10.1051/itmconf/20203403006
Search in Google Scholar Back to article
[6] A. Diamandescu, On the Ψ instability of a nonlinear Lyapunov matrix differential equations, An. Univ. Vest Timiş., Ser. Mat.-Inform. XLIX (1) (2011), 21–37.
Search in Google Scholar Back to article
[7] A. Diamandescu, On Ψ- Bounded Solutions for a nonlinear Lyapunov Matrix Differential Equation on ℝ, An. Univ. Vest Timiş., Ser. Mat.-Inform. LVI (2) (2018), 131–150.10.2478/awutm-2018-0020
Search in Google Scholar Back to article
[8] A. Diamandescu, Note on the Ψ-asymptotic relationships between Ψ-bounded solutions of two Lyapunov matrix differential equations, Int. J. Nonlinear Anal. Appl. 13 (2) (2022), 2361–2372.
Search in Google Scholar Back to article
[9] A. Diamandescu, On the Ψ-Conditional Exponential Asymptotic Stability of a Nonlinear Lyapunov Matrix Differential Equation with Integral Term as Right Side, An. Univ. Vest Timiş., Ser. Mat.-Inform. 58 (1), (2022), 56–75.10.2478/awutm-2022-0005
Search in Google Scholar Back to article
[10] T. G. Hallam, On asymptotic equivalence of the bounded solutions of two systems of differential equations, Michigan Math. J. 16 (1969), 353–363.10.1307/mmj/1029000319
Search in Google Scholar Back to article
[11] J. R. Magnus, H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, John Wiley & Sons Ltd, Chichester, 1999.
Search in Google Scholar Back to article
[12] I. M. Olaru, The Asymptotic Equivalence of the Differential Equations with Modified Argument, Acta Univ. Apulensis, Math. Inform. 11 (2006), 211–217.
Search in Google Scholar Back to article
[13] I. A. Rus, Generalized contractions, Seminar on fixed point theory 3 (1983), 1–130.
Search in Google Scholar Back to article
[14] V. A, Staikos, A note on the boundedness of solutions of ordinary differential equations, Boll. Unione Mat. Ital. S. IV 1 (1968), 256–261.
Search in Google Scholar Back to article
[15] P. Talpalaru, Quelques problemes concernant l equivalence asymptotique des systemes differentiels, Boll. Unione Mat. Ital. S. IV 4 (1971) 164–186.
Search in Google Scholar Back to article

The Ψ–Asymptotic Equivalence of the Lyapunov Matrix Differential Equations with Integral Term as Right Side and Modified Argument

Abstract

Paradigm

My account