Qualitative behavior of solutions of difference equations with several oscillating coefficients
Tóm tắt
Sufficient conditions which guarantee the convergence of the nonoscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.
Tài liệu tham khảo
Agarwal, R.P.; Bohner, M.; Grace, S.R.; O’ Regan, D.: Discrete Oscillation Theory. Hindawi Publishing Corporation, New York (2005)
Berezansky L., Braverman E.: On exponential stability of a linear differential equation with an oscillating coefficient. Appl. Math. Lett. 22, 1833–1837 (2009)
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)
Fukagai N., Kusano T.: Oscillation theory of first order functional-differential equations with deviating arguments. Annl. Mat. Pura Appl. 136, 95–117 (1984)
Gyori, I.; Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford (1991)
Khatibzadeh H.: An oscillation criterion for a delay difference equation. Comput. Math. Appl. 57, 37–41 (2009)
Kulenovic M.R., Grammatikopoulos M.K.: First order functional differential inequalities with oscillating coefficients. Nonlinear Anal. 8, 1043–1054 (1984)
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)
Lakshmikantham, V.; Trigiante, D.: Theory of Difference Equations: Numerical Methods and Applications. Mathematics in Science and Engineering, vol. 181. Academic Press, Boston (1998)
Li X., Zhu D., Wang H.: Oscillation for advanced differential equations with oscillating coefficients. Internat. J. Math. Math. Sci. 33, 2109–2118 (2003)
Qian C., Ladas G., Yan J.: Oscillation of difference equations with oscillating coefficients. Radovi Mathematicki 8, 55–65 (1992)
Tang X.H., Cheng S.S.: An oscillation criterion for linear difference equations with oscillating coefficients. J. Comput. Appl. Math. 132, 319–329 (2001)
Xianhua T.: Oscillation of first order delay differential equations with oscillating coefficients. Appl. Math. J. Chin. Univ. Ser. B 15, 252–258 (2000)
Yan W., Yan J.: Comparison and oscillation results for delay difference equations with oscillating coefficients. Internat. J. Math. Math. Sci. 19, 171–176 (1996)
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)
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)
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)
Zhou X.: Oscillatory and asymptotic properties of higher order nonlinear neutral difference equations with oscillating coefficients. Appl. Math. Lett. 21, 1142–1148 (2008)
Zhou X., Yu R.: Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients. Comput. Math. Appl. 56, 1562–1568 (2008)