On connections between oscillatory solutions of functional, difference and differential equations

• Autorzy: Nowakowska W. , Werbowski J.
• Języki publikacji: EN

Abstrakty

EN

The paper contains connections between oscillation of solutions of iterative functional equations, difference equations and differential equations with advanced or delayed arguments. New oscillatory criteria for these equations are given.

Słowa kluczowe

EN

oscillatory solution; difference equation; differential equations

PL

równanie funkcyjne; równanie różnicowe; równania różniczkowe

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 95--106
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Nowakowska W.

autor

Werbowski J.

• Poznań University of Technology Institute of Mathematics Piotrowo 3A, 60-965 Poznań, Poland,

Bibliografia

• [1] Agarwal R.P., Bohner M., Grace S.R., O’Regan D., Discrete Oscillation Theory, Hindawi Publishing Corporation, 2005.
• [2] Agarwal R.P., Grace S.R., O’Regan D., Oscillation Theory for Difference and Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, Boston, London, 2000.
• [3] Domshlak Y., Discrete version of Sturmian Comparison Theorem for non symmetric equations, Doklady Azerb. Acad. Sci., 37(1981), 12-15. (in Russian).
• [4] Erbe L.H., Kong Q., Zhang B.G., Oscillation Theory for Functional-Differential Equations, Marcel Dekker, Inc., New York, 1995.
• [5] Erbe L.H., Zhang B.G., Oscillation of discrete analogues of delay equations, Differential Integral Equations, 2(1989), 300 309.
• [6] Golda W., Werbowski J., Oscillation of linear functional equations of the second order, Funkcial. Ekvac., 37(1994), 221 227.
• [7] Györi I., Ladas G., Oscillation theory of delay differential equations with applications, Clarendon Press, Oxford, 1991.
• [8] Kneser A., Untersuchungen über die reelen Nullstellen der Integrale linearer Differentialgleichungen, Math. Ann., 42(3)(1893), 409-435.
• [9] Koplatadze R.G., Chanturia T.A., On oscillatory properties of differential equations with a deviating argument, Izdat. Tbilis. Univ., Tbilisi, 1977. (in Russian).
• [10] Koplatadze R.G., Chanturia T.A., On oscillatory and monotonic solutions of first order differential equations with deviating arguments, Differential’nye Uravnenija, 18(1982), 1463-1465. (in Russian).
• [11] Koplatadze R.G., Criteria for the oscillation of solutions of differential inequalities and second-order equations with retarded argument, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy, 17(1986), 104-121. (in Russian).
• [12] Kuczma M., Choczewski B., Ger R., Iterative functional equations, Cambridge University Press, Cambridge, 1990.
• [13] Ladas G., Sharp conditions for oscillations caused by delays, Appl. Anal., 9(1979), 93-98.
• [14] Ladas G., Philos Ch.G., Sficas Y.G., Sharp conditions for the oscillation for delay difference equations, Appl. Math. Simulation J., 2(1989), 101-111.
• [15] Ladas G., Lakshmikantham V., Papadakis L.S., Oscillations of higherorder retarded differential equations generated by the retarded arguments in Delay and Functional Differential Equations and Their Applications, Academic Press, New York, (1972), 219-231.
• [16] Ladde G.S., Lakshmikantham G.S., Zhang B.G., Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, Inc., New York, 1987.
• [17] Lakshmikantham V, Trigiante D., Theory of Difference Equations: Numerical Methods and Applications, Academic Press, Inc., San Diego, 1988.
• [18] Myshkis A.D., Linear homogeneous differential equations of first order with deviating arguments, Uspekhi Mat. Nauky, 5(1950), 160-162. (in Russian).
• [19] Nowakowska W, Werbowski J., Oscillation of linear functional equations of higher order, Arch.Math., 31(1995), 251-258.
• [20] Nowakowska W, Werbowski J., Oscillatory behavior of solutions of linear recurrence equations, J. Differ. Equations Appl., 1(1995), 239-247.
• [21] Nowakowska W, Werbowski J., Oscillatory behavior of solutions of functional equations, Nonlinear Anal., 44(2001), 767-775.
• [22] Nowakowska W, Werbowski J., Oscillatory solutions of linear iterative functional equations, Indian J. Pure Appl. Math., 35(4)(2004), 429-439.
• [23] Shen J., Stavroulakis I.P., Sharp conditions for nonoscillation of functional equations, Indian J. Pure Appl. Math., 33(4)(2002), 543-554.
• [24] Shevelo V.N., Oscillation of Solutions of Differential Equations with Deviating Arguments, Naukowa Dumka, Kiev, 1978. (in Russian).
• [25] Stavroulakis I.P., Oscillation criteria for delay and difference equations, Stud. Univ. Žilina Math. Ser., 17(1)(2003), 161-176.
• [26] Sturm C., Mémoire sur les équations différentielles linéaires de second ordre, J. Math. Pura Appl., 1(1836), 101-186.
• [27] Thandapani E., Ravi K., Oscillation of nonlinear functional equations, Indian J. Pure Appl. Math., 30(12)(1999), 1235 1241.
• [28] Werbowski J., Oscillations of first-order differential inequalities with deviating arguments, Ann. Mat. Pura Appl., 140(1985), 383-392.
• [29] Werbowski J., Oscillations of first order linear differential equations with delay, Proceedings of the Conference on Ordinary Differential Equations, July 1996, Poprad, Slovak Republic.