References
- [1] CHATZARAKIS, G. E.-KOPLATADZE, R.-STAVROULAKIS, I. P.: Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal. 68 (2008), 994-1005.10.1016/j.na.2006.11.055
- [2] CHATZARAKIS, G. E.-KOPLATADZE, R.-STAVROULAKIS, I. P.: Optimal oscillation criteria for the first order difference equations with delay argument, Pacific J. Math. 235 (2008), 15-33.10.2140/pjm.2008.235.15
- [3] CHATZARAKIS, G. E.-PHILOS, CH. G.-STAVROULAKIS, I. P.: On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differential Equations 2008 (2008), No. 4, 1-15.
- [4] CHATZARAKIS,G. E.-PHILOS, CH. G.-STAVROULAKIS, I. P.: An oscillation criterion for linear difference equations with general delay argument, Port. Math. (to appear).
- [5] CHATZARAKIS, G. E.-STAVROULAKIS, I. P.: Oscillations of first order linear delay difference equations, Austral. J. Math. Anal. Appl. 3 (2006), No. 1, Art. 14, pp. 11.
- [6] CHEN, M. P.-YU, Y. S.: Oscillations of delay difference equations with variable coefficients, in: Proc. of the 1st Internat. Conference on Difference Equations (S. N. Elaydi et al., eds.), Trinity Univ., San Antonio, TX, USA, May 25-28, 1994, Gordon and Breach, London, 1995, pp. 105-114.
- [7] CHENG, S. S.-ZHANG, B. G.: Qualitative theory of partial difference equations (I): Oscillation of nonlinear partial difference equations, Tamkang J. Math. 25 (1994), 279-298.10.5556/j.tkjm.25.1994.4455
- [8] CHENG, S. S.-LIU, S. T.-ZHANG, G.: A multivariate oscillation theorem, Fasc. Math. 30 (1999), 15-22.
- [9] CHENG, S. S.-XI, S. L.-ZHANG, B. G.: Qualitative theory of partial difference equations (II): Oscillation criteria for direct control system in several variables, Tamkang J. Math. 26 (1995), 65-79.10.5556/j.tkjm.26.1995.4380
- [10] CHENG, S. S.-ZHANG, G.: “Virus” in several discrete oscillation theorems, Appl. Math. Lett. 13 (2000), 9-13.10.1016/S0893-9659(99)00178-0
- [11] DIBLIK, J.: Positive and oscillating solutions of differential equations with delay in critical case, J. Comput. Appl. Math. 88 (1998), 185-202.10.1016/S0377-0427(97)00217-3
- [12] DOMSHLAK, Y.: A discrete analogue of the Sturm comparison theorem for nonsymmetric equations, Dokl. Akad. Nauk Azerbaidzhana 37 (1981), 12-15. (In Russian)
- [13] DOMSHLAK, Y.: Sturm’s Comparison Method in the Investigation of Behavior of the Solutions of Operator Differential Equations, “Elm”, Baku, USSR, 1986. (In Russian)
- [14] DOMSHLAK, Y.: Oscillatory properties of linear difference equations with continuous time, Differential Equations Dynam. Systems 4 (1993), 311-324.
- [15] DOMSHLAK, Y.: Sturmian comparison method in oscillation study for discrete difference equations, I, Differential Integral Equations 7 (1994), 571-582.
- [16] DOMSHLAK, Y.: On oscillation properties of delay differencial equations with oscillating coefficients, Funct. Differ. Equ. 2 (1994), 59-68.
- [17] DOMSHLAK, Y.: Delay-difference equations with periodic coefficients: sharp results in oscillation theory, Math. Inequal. Appl. 1 (1998), 403-422.
- [18] DOMSHLAK, Y.:What should be a discrete version of the Chanturia-Koplatadze lemma? Funct. Differ. Equ. 6 (1999), 299-304.
- [19] DOMSHLAK, Y.: Riccati difference Equations with almost periodic coefficients in the critical state, Dynam. Systems Appl. 8 (1999), 389-399.
- [20] DOMSHLAK, Y.: The Riccati difference equations near “extremal” critical states, J. Difference Equ. Appl. 6 (2000), 387-416.10.1080/10236190008808237
- [21] DOMSHLAK, Y.-ALIEV, A.: On oscillatory properties of the first order differential equations with one or two retarded arguments, Hiroshima Math. J. 18 (1998), 31-46.
- [22] DOMSHLAK, Y.-STAVROULAKIS, I. P.: Oscillations of first-order delay differential equations in a critical state, Appl. Anal. 61 (1996), 359-377.10.1080/00036819608840464
- [23] ELBERT, A.-STAVROULAKIS, I. P.: Oscillations of first order differential equations with deviating arguments, Univ. of Ioannina T.R. No. 172, 1990, in: Recent Trends in Differential Equations (R. P. Agarwal, ed.), World Sci. Ser. Appl. Anal.,Vol. 1, World Sci. Publishing Co., Singapore, 1992, pp. 163-178.
- [24] ELBERT, A.-STAVROULAKIS, I. P.: Oscillation and nonoscillation criteria for delay differential equations, Proc. Amer. Math. Soc. 123 (1995), 1503-1510.10.1090/S0002-9939-1995-1242082-1
- [25] ERBE, L. H.-KONG, Q.-ZHANG, B. G.: Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York, 1995.
- [26] ERBE, L. H.-ZHANG, B. G.: Oscillation of first order linear differential equations with deviating arguments, Differential Integral Equations 1 (1988), 305-314.
- [27] ERBE, L. H.-ZHANG, B. G.: Oscillation of discrete analogues of delay equations, Differential Integral Equations 2 (1989), 300-309.10.57262/die/1372428799
- [28] FUKAGAI, N.-KUSANO, T.: Oscillation theory of first order functional differential equations with deviating arguments, Ann. Mat. Pura Appl. (4) 136 (1984), 95-117.10.1007/BF01773379
- [29] GOPALSAMY, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Math. Appl., Vol. 74, Kluwer Acad. Publ., Dordrecht, 1992.10.1007/978-94-015-7920-9
- [30] GYORI, I.-LADAS, G.: Oscillation Theory of Delay Differential Equations with Applications. Clarendon Press, Oxford, 1991.
- [31] HALE, J. K.: Theory of Functional Differential Equations (2nd ed.), Appl. Math. Sci., Vol. 3, Springer, New York, 1997.
- [32] IVANOV, A. F.-SHEVELO, V. N.: Oscillation and asymptotic behavior of solutions of first order differential equations, Ukra¨ın. Math. Zh. 33 (1981), 745-751, 859.
- [33] JAROˇS, J.-STAVROULAKIS, I. P.: Necessary and sufficient conditions for oscillations of difference equations with several delays, Util. Math. 45 (1994), 187-195.
- [34] JAROˇS, J.-STAVROULAKIS, I. P.: Oscillation tests for delay equations, Rocky Mountain J. Math. 29 (1999), 139-145.
- [35] JIAN, C.: Oscillation of linear differential equations with deviating argument, Math. Practice Theory 1 (1991), 32-41. (In Chinese)
- [36] KON, M.-SFICAS, Y. G.-STAVROULAKIS, I. P.: Oscillation criteria for delay equations, Proc. Amer. Math. Soc. 128 (2000), 2989-2997.10.1090/S0002-9939-00-05530-1
- [37] KOPLATADZE, R. G.-CHANTURIJA, T. A.: On the oscillatory and monotonic solutions of first order differential equations with deviating arguments, Differentsial’nye Uravneniya 18 (1982), 1463-1465.
- [38] KOPLATADZE, R. G.-KVINIKADZE, G.: On the oscillation of solutions of first order delay differential inequalities and equations, Georgian Math. J. 1 (1994), 675-685.10.1007/BF02254685
- [39] KOZAKIEWICZ, E.: Conditions for the absence of positive solutions of first order differential inequalities with deviating agruments, in: Proc. of the 4th Internat. Colloq. On Differ. Equ. (D. Bainov, et al., eds.), Plovdiv, Bulgaria, August 18-22, 1993, VSP, Utrecht, 1994, pp. 157-161.10.1515/9783112318874-017
- [40] KULENOVIC, M. R.-GRAMMATIKOPOULOS, M. K.: First order functional differential inequalities with oscillating coefficients, Nonlinear Anal. 8 (1984), 1043-1054.10.1016/0362-546X(84)90098-1
- [41] KWONG, M. K.: Oscillation of first order delay equations, J. Math. Anal. Appl. 156 (1991), 374-286.10.1016/0022-247X(91)90396-H
- [42] LADAS, G.: Sharp conditions for oscillations caused by delay, Appl. Anal. 9 (1979), 93-98.10.1080/00036817908839256
- [43] LADAS, G.: Recent developments in the oscillation of delay difference equations, in: Proc. Int. Conf. on Differential Equations: Stability and Control, Colorado Springs, CO, USA, 1989, Lect. Notes Pure Appl. Math. 127, Dekker, New York, 1990, pp. 321-332.
- [44] LADAS, G.-LASKHMIKANTHAM, V.-PAPADAKIS, J. S.: Oscillations of higherorder retarded differential equations generated by retarded argument, Delay Functional Diff. Equ. Appl., Conf. Park City, Utah, 1972, Academic Press, New York, 1972, pp. 219-231.10.1016/B978-0-12-627250-5.50013-7
- [45] LADAS, G.-PAKULA, L.-WANG, Z. C.: Necessary and sufficient conditions for the oscillation of difference equations, Panam. Math. J. 2 (1992), 17-26.
- [46] LADAS, G.-PHILOS, CH. G.-SFICAS, Y. G.: Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation 2 (1989), 101-112.10.1155/S1048953389000080
- [47] LADAS, G.-QIAN, C.-YAN, J.: A comparison result for the oscillation of delay differential equations, Proc. Amer. Math. Soc. 114 (1992), 939-946.10.1090/S0002-9939-1992-1052575-5
- [48] LADAS, G.-SFICAS, Y. G.-STAVROULAKIS, I. P.: Functional-differential inequalities and equations with oscillating coefficients, in: Proc. Internat. Conf.-Trends in Theory and Practice of Nonlinear Differential Equations, Arlington, Texas, USA, 1982, Lecture Notes in Pure and Appl. Math., Vol. 90, Marcel Dekker, New York, 1984, pp. 277-284.
- [49] LADDE, G. S.: Oscillations caused by retarded perturbations of first order linear ordinary differential equations, Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 63 (1977), 351-359.
- [50] LADDE, G. S.: Class of functional equations with applications, Nonlinear Anal. 2 (1978), 259-261.10.1016/0362-546X(78)90073-1
- [51] LADDE, G. S.: Stability and oscillation in single-species processes with past memory, Internat. J. Systems Sci. 10 (1979), 621-647.10.1080/00207727908941607
- [52] LADDE, G. S.-LAKSHMIKANTHAM, V.-ZHANG, B. G.: Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker, New York, 1987.
- [53] LALLI, B.-ZHANG, B. G.: Oscillation of difference equations, Colloq. Math. 65 (1993), 25-32.10.4064/cm-65-1-25-32
- [54] LI, B.: Oscillations of delay differential equations with variable coefficients, J. Math. Anal. Appl. 192 (1995), 312-321.10.1006/jmaa.1995.1173
- [55] LI, B.: Oscillations of first order delay differential equations, Proc. Amer. Math. Soc. 124 (1996), 3729-3737.10.1090/S0002-9939-96-03674-X
- [56] LUO, Z.-SHEN, J. H.: New results for oscillation of delay difference equations, Comput. Math. Appl. 41 (2001), 553-561.10.1016/S0898-1221(00)00298-4
- [57] LUO, Z.-SHEN, J. H.: New oscillation criteria for delay difference equations, J. Math. Anal. Appl. 264 (2001), 85-95.10.1006/jmaa.2001.7641
- [58] MYSHKIS, A. D.: Linear homogeneous differential equations of first order with deviating arguments, Uspekhi Mat. Nauk 5 (1950), 160-162. (In Russian)
- [59] PHILOS, CH. G.-SFICAS, Y. G.: An oscillation criterion for first-order linear delay differential equations, Canad. Math. Bull. 41 (1998), 207-213.10.4153/CMB-1998-030-3
- [60] SFICAS, Y. G.-STAVROULAKIS, I. P.: Oscillation criteria for first-order delay equations, Bull. London Math. Soc. 35 (2003), 239-246.10.1112/S0024609302001662
- [61] SHEN, J. H.-LUO, Z.: Some oscillation criteria for difference equations, Comput. Math. Appl. 40 (2000), 713-719.10.1016/S0898-1221(00)00190-5
- [62] SHEN, J. H.-STAVROULAKIS, I. P.: Oscillation criteria for delay difference equations, Electron. J. Differential Equations 2001 (2001), No. 10, 1-15.
- [63] STAVROULAKIS, I. P.: Oscillations of delay difference equations, Comput. Math. Appl. 29 (1995), 83-88.10.1016/0898-1221(95)00020-Y
- [64] STAVROULAKIS, I. P.: Oscillation criteria for first order delay difference equations, Mediterr. J. Math. 1 (2004), 231-240.10.1007/s00009-004-0013-7
- [65] TANG, X. H.: Oscillations of delay difference equations with variable coefficients, J. Central So. Univ. Technology 29 (1998), 287-288. (In Chinese)
- [66] TANG, X. H.: Oscillation of delay differential equations with variable coefficients, J. Math. Study 31 (1998), 290-293.
- [67] TANG, X. H.-CHENG, S. S.: An oscillation criterion for linear difference equations with oscillating coefficients, J. Comput. Appl. Math. 132 (2001), 319-329.10.1016/S0377-0427(00)00436-2
- [68] TANG, X. H.-YU, J. S.: Oscillation of delay difference equations, Comput. Math. Appl. 37 (1999), 11-20.10.1016/S0898-1221(99)00083-8
- [69] TANG, X. H.-YU, J. S.: A further result on the oscillation of delay difference equations, Comput. Math. Appl. 38 (1999), 229-237.10.1016/S0898-1221(99)00301-6
- [70] TANG, X. H.-YU, J. S.: Oscillations of delay difference equations in a critical state, Appl. Math. Lett. 13 (2000), 9-15.10.1016/S0893-9659(99)00158-5
- [71] TANG, X. H.-YU, J. S.: Oscillation of delay difference equations, Hokkaido Math. J. 29 (2000), 213-228.10.14492/hokmj/1350912965
- [72] TANG, X. H.-YU, J. S.: Oscillation of first order delay differential equations, J. Math. Anal. Appl. 248 (2000), 247-259.10.1006/jmaa.2000.6894
- [73] TANG, X. H.-YU, J. S.: Oscillations of first order delay differential equations in a critical state, Mathematica Applicata 13 (2000), 75-79.
- [74] TANG, X. H.-YU, J. S.: Oscillation of first order delay differential equations with oscillating coefficients, Appl. Math., J. Chin. Univ. 15 (2000), 252-258.
- [75] TANG, X. H.-YU, J. S.: New oscillation criteria for delay difference equations, Comput. Math. Appl. 42 (2001), 1319-1330.10.1016/S0898-1221(01)00243-7
- [76] TANG, X. H.-YU, J. S.-WANG, Z. C.: Comparison theorems of oscillation of first order delay differential equations in a critical state with applications, Ke Xue Tongbao 44 (1999), 26-30.
- [77] TOMARAS, A.: Oscillatory behaviour of an equation arising from an industrial problem, Bull. Austral. Math. Soc. 13 (1975), 255-260.10.1017/S0004972700024448
- [78] TOMARAS, A.: Oscillations of a first order functional differential equation, Bull. Austral. Math. Soc. 17 (1977), 91-95.10.1017/S0004972700025491
- [79] TOMARAS, A.: Oscillatory behaviour of first order delay differential equations, Bull. Austral. Math. Soc. 19 (1978), 183-190.10.1017/S0004972700008662
- [80] WANG, Z. C.-STAVROULAKIS, I. P.-QIAN, X. Z.: A Survey on the oscillation of solutions of first order linear differential equations with deviating arguments, Appl. Math. E-Notes 2 (2002), 171-191.
- [81] YAN, W.-YAN, J.: Comparison and oscillation results for delay difference equations with oscillating coefficients, Int. J. Math. Math. Sci. 19 (1996), 171-176.10.1155/S0161171296000245
- [82] YU, J. S.-TANG, X. H.: Comparison theorems in delay differential equations in a critical state and application, Proc. London Math. Soc. (3) 63 (2001), 188-204.10.1112/S0024610700001599
- [83] YU, J. S.-WANG, Z. C.: Some further results on oscillation of neutral differential equations, Bull. Austral. Math. Soc. 46 (1992), 149-157.10.1017/S0004972700011758
- [84] YU, J. S.-WANG, Z. C.-ZHANG, B. G.-QIAN, X. Z.: Oscillations of differential equations with deviting arguments, Panam. Math. J. 2 (1992), 59-78.
- [85] YU, J. S.-ZHANG, B. G.-QIAN, X. Z.: Oscillations of delay difference equations with oscillating coefficients, J. Math. Anal. Appl. 177 (1993), 432-444.10.1006/jmaa.1993.1267
- [86] YU, J. S.-ZHANG, B. G.-WANG, Z. C.: Oscillation of delay difference equations, Appl. Anal. 53 (1994), 117-124.10.1080/00036819408840248
- [87] ZHANG, B. G.-LIU, S. T.-CHENG, S. S.: Oscillation of a class of delay partial difference equations, J. Difference Equ. Appl. 1 (1995), 215-226.10.1080/10236199508808022
- [88] ZHANG, B. G.-ZHOU, Y.: The semicycles of solutions of delay difference equations, Comput. Math. Appl. 38 (1999), 31-38.10.1016/S0898-1221(99)00235-7
- [89] ZHANG, B. G.-ZHOU, Y.: Comparison theorems and oscillation criteria for difference equations, J. Math. Anal. Appl. 247 (2000), 397-409.10.1006/jmaa.2000.6833
- [90] ZHOU, Y.-YU, Y. H.: On the oscillation of solutions of first order differential equations with deviating arguments, Acta Math. Appl. Sinica 15 (1999), 288-302.