×

Qualitative behavior of solutions of difference equations with several oscillating coefficients. (English) Zbl 1317.39017

This paper investigates the convergence and oscillatory behavior of solutions of retarded or advanced difference equations with several deviating arguments and oscillating coefficients, and presents some sufficient conditions. Four examples are given to illustrate the main results.

MSC:

39A21 Oscillation theory for difference equations
39A10 Additive difference equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Agarwal, R.P.; Bohner, M.; Grace, S.R.; O’ Regan, D.: Discrete Oscillation Theory. Hindawi Publishing Corporation, New York (2005) · Zbl 1084.39001
[2] Berezansky L., Braverman E.: On exponential stability of a linear differential equation with an oscillating coefficient. Appl. Math. Lett. 22, 1833-1837 (2009) · Zbl 1187.34096 · doi:10.1016/j.aml.2009.07.007
[3] Bolat Y., Akin Ö.: Oscillatory behavior of a higher-order nonlinear neutral type functional difference equation with oscillating coefficients. Appl. Math. Lett. 17, 1073-1078 (2004) · Zbl 1069.39007 · doi:10.1016/j.aml.2004.07.011
[4] Fukagai N., Kusano T.: Oscillation theory of first order functional-differential equations with deviating arguments. Annl. Mat. Pura Appl. 136, 95-117 (1984) · Zbl 0552.34062 · doi:10.1007/BF01773379
[5] Gyori, I.; Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford (1991) · Zbl 0780.34048
[6] Khatibzadeh H.: An oscillation criterion for a delay difference equation. Comput. Math. Appl. 57, 37-41 (2009) · Zbl 1165.39305 · doi:10.1016/j.camwa.2008.07.041
[7] Kulenovic M.R., Grammatikopoulos M.K.: First order functional differential inequalities with oscillating coefficients. Nonlinear Anal. 8, 1043-1054 (1984) · Zbl 0512.34054 · doi:10.1016/0362-546X(84)90098-1
[8] Ladas, G.; Sficas, G.; Stavroulakis, I.P.: Functional-differential inequalities and equations with oscillating coefficients. Trends in theory and practice of nonlinear differential equations (Arlington, Tex., 1982). In: Lecture Notes in Pure and Applied Mathematics, vol. 90. pp. 277-284. Dekker, New York (1984) · Zbl 0955.39002
[9] Lakshmikantham, V.; Trigiante, D.: Theory of Difference Equations: Numerical Methods and Applications. Mathematics in Science and Engineering, vol. 181. Academic Press, Boston (1998) · Zbl 1014.39001
[10] Li X., Zhu D., Wang H.: Oscillation for advanced differential equations with oscillating coefficients. Internat. J. Math. Math. Sci. 33, 2109-2118 (2003) · Zbl 1031.34066 · doi:10.1155/S0161171203209030
[11] Qian C., Ladas G., Yan J.: Oscillation of difference equations with oscillating coefficients. Radovi Mathematicki 8, 55-65 (1992) · Zbl 0955.39002
[12] Tang X.H., Cheng S.S.: An oscillation criterion for linear difference equations with oscillating coefficients. J. Comput. Appl. Math. 132, 319-329 (2001) · Zbl 0984.65135 · doi:10.1016/S0377-0427(00)00436-2
[13] Xianhua T.: Oscillation of first order delay differential equations with oscillating coefficients. Appl. Math. J. Chin. Univ. Ser. B 15, 252-258 (2000) · Zbl 0971.34053 · doi:10.1007/s11766-000-0048-x
[14] Yan W., Yan J.: Comparison and oscillation results for delay difference equations with oscillating coefficients. Internat. J. Math. Math. Sci. 19, 171-176 (1996) · Zbl 0840.39006 · doi:10.1155/S0161171296000245
[15] Yu J.S., Tang X.H.: Sufficient conditions for the oscillation of linear delay difference equations with oscillating coefficients. J. Math. Anal. Appl. 250, 735-742 (2000) · Zbl 0964.39011 · doi:10.1006/jmaa.2000.7120
[16] Yu J.S., Zhang B.G., Qian X.Z.: Oscillations of delay difference equations with oscillating coefficients. J. Math. Anal. Appl. 177, 432-444 (1993) · Zbl 0787.39004 · doi:10.1006/jmaa.1993.1267
[17] Zhang G., Cheng S.S.: Elementary oscillation criteria for a three term recursive relation with oscillating coefficient sequence. Tamkang J. Math. 29, 227-232 (1998) · Zbl 0915.39007
[18] Zhou X.: Oscillatory and asymptotic properties of higher order nonlinear neutral difference equations with oscillating coefficients. Appl. Math. Lett. 21, 1142-1148 (2008) · Zbl 1158.39010 · doi:10.1016/j.aml.2007.12.012
[19] Zhou X., Yu R.: Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients. Comput. Math. Appl. 56, 1562-1568 (2008) · Zbl 1155.34345 · doi:10.1016/j.camwa.2008.03.006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.