On the asymptotic equivalence of a differential system with maxima


In this paper, we give some general results on the asymptotic relationship between the solutions of a linear differential system and its perturbed differential system with maxima. Also, we present an example to illustrate our results.


D. Otrocol
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,


Differential equations with maxima; Dhage iteration method; hybrid fixed point theorem; approximation of solutions

Cite this paper as:

D. Otrocol, On the asymptotic equivalence of a differential system with maxima, Rend. Circ. Mat. Palermo (2), Vol. 65(2016) no. 3, pp. 387-393.


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Rendiconti del Circolo Matematico di Palermo

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[1] Bainov, D.D., Hristova, S., Differential equations with maxima, Pure and applied mathematics. Chapman & Hall/CRC (2011)Google Scholar

[2] Bainov, D.D., Kazakova, N.G.,  A finite difference method for solving the periodic problem for autonomous differential equations with maxima. Math. J. Toyama Univ. 15, 1–13 (1992)MathSciNetzbMATHGoogle Scholar

[3] Besekerski, V.A., Popov, E.P., Theory of automatic regulation system. Nauka, Moskov (1975). (in Russian)Google Scholar

[4] Diamandescu, A., Note on the ψψ-boundedness of the solutions of a system of differential equations. Acta Math. Univ. Comenianae 73(2), 223–233 (2004)MathSciNetzbMATHGoogle Scholar

[5] Georgiev, L., Angelov, V.G., On the existence and uniqueness of solutions for maximum equations. Glasnik Matematički 37(2), 275–281 (2002)MathSciNetzbMATHGoogle Scholar

[6] Gonzáles, P., Pinto, M., Component-wise conditions for the asymptotic equivalence for nonlinear differential equations with maxima. Dyn. Syst. Appl. 20, 439–454 (2011)zbMATHGoogle Scholar

[7] Otrocol, D., Rus, I.A., Functional-differential equations with “maxima” via weakly Picard operators theory. Bull. Math. Soc. Sci. Math. Roumanie 51(99), 253–261 (2008)Google Scholar

[8] Otrocol, D., Rus, I.A., Functional-differential equations with maxima of mixed type argument. Fixed Point Theory 9(1), 207–220 (2008)MathSciNetzbMATHGoogle Scholar

[9] Otrocol, D., Properties of the solutions of system of differential equations with maxima, via weakly Picard operator theory. Commun. Appl. Anal. 17(1), 99–107 (2013)MathSciNetzbMATHGoogle Scholar

[10] Otrocol, D., Systems of functional differential equations with maxima, of mixed type. Electron. J. Qual. Theory Differ. Equ. 2014(5), 1–9 (2014)Google Scholar

[11] Otrocol, D., Ilea, V.A., Qualitative properties of functional differential equation. Electron. J. Qual. Theory Differ. Equ. 2014(47), 1–8 (2014)Google Scholar

[12] Olaru, M., Olaru, V.,  CgCg asymptotic equivalence for some functional equation of type Volterra. Gen. Math. 14(1), 31–40 (2006)MathSciNetzbMATHGoogle Scholar

[13] Piccinini, L.C., Stampacchia, G., Vidossich, G., Ordinary differential equations in RnRn. Springer-Verlag (1984)Google Scholar

[14] Stepanov, E., On solvability of some boundary value problems for differential equations with ”maxima”. Topol. Methods Nonlinear Anal. 8, 315–326 (1996)Google Scholar

[15] Talpalaru, P., On stability of non-linear differential systems. Bul. Inst. Pol. Iaşi 27(1–2), 43–48 (1977)MathSciNetzbMATHGoogle Scholar

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