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Article

Keywords:
asymptotic equivalence; difference inequalities
Summary:
Using the method of variation of constants, discrete inequalities and Tychonoff’s fixed-point theorem we study problem asymptotic equivalence of second order difference equations.
References:
[1] Brauer, F., Wang, J. S.: On the asymptotic relationship between solutions of two systems of ordinary differential equation. J. Differential Equations 6 (1969), 527–543. MR 0252765
[2] Hallam, T. G.: Asymptotic relationskips between the solutions of two second order differential equations. Ann. Polon. Math. 24 (1971), 295–300. MR 0301316
[3] Lakshmikantham, V., Leela, S.: Differential and Integral Ineqalities. vol. I, New York and London, Academic Press 1969.
[4] Morchało, J.: Asymptotic equivalence of Volterra difference systems. Publ. Mat. 39 (1995), 301–312. MR 1370888
[5] Morchało, J.: Asymptotic equivalence of difference equations. Math. Slovaca 48 (1998), 57–68. MR 1635239
[6] Morchało, J.: Asymptotic equivalence of second-order difference equations. J. Math. Anal. Appl. 238 (1999), 91–100. MR 1711480
[7] Onuchic, N.: Relationship among the solutions of two systems or ordinary differential equation. Michigan Math. J. 10 (1963), 129–139. MR 0165192
[8] Ráb, M.: Asymptotic relationships between the solutions of two systems of differential equations. Ann. Polon. Math. 30 (1974), 119–124. MR 0355217
[9] Svec, M.: Asymptotic relationship between solutions of two systems of differential equations. Czechoslovak Math. J. 24 (99), No. 1 (1974), 44–58. MR 0348202 | Zbl 0322.34037
[10] Talpalaru, P.: Asymptotic behaviour of perturbed difference equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Ser. VIIILXIV (1979), 563–571. MR 0561940 | Zbl 0441.39006
[11] Kuben, J.: Asymptotic equivalence of second order differential equations. Czechoslovak Math. J. 34 (109) (1984), 189–201. MR 0743485 | Zbl 0555.34048
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