Uneingeschränkter Zugang

Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations


Zitieren

[1] ADIVAR, M.— KOYUNCUOĞLU, H.C.—RAFFOUL, Y.N.: Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay, J. Difference Equ. Appl. 19 (2013), no.12, 1927–1939, doi10.1080/10236198.2013.791688. Search in Google Scholar

[2] AGARWAL, R.—GRACE, S.: Oscillation of higher-order nonlinear difference equations of neutral type, Appl. Math. Lett. 12 (1999), no. 8, 77–83, doi:10.1016/S0893- -9659(99)00126-3. Search in Google Scholar

[3] AGARWAL, R.—THANDAPANI, E. —WONG, P.: Oscillation of higher-order neutral difference equation, Appl. Math. Lett. 10 (1997), no.1, 71–78, doi:10.1016/S0893- 9659(96)00114-0. Search in Google Scholar

[4] ANDRUCH-SOBIŁO, A.—MIGDA, M.: On the rational recursive sequence xn+1=axn1b+cxnxn1 \[{x_{n + 1}} = \frac{{a{x_{n - 1}}}}{{b + c{x_n}{x_{n - 1}}}}\] , Tatra Mt. Math. Publ. 43 (2009) 1–9, doi:10.2478/v10127-009-0020-y.10.2478/v10127-009-0020-y Search in Google Scholar

[5] BOLAT, Y.—AKIN, Ö.: Oscillatory behaviour of a higher-order nonlinear neutral type functional difference equation with oscillating coefficients, Appl. Math. Lett. 17 (2004), no. 9, 1073–1078, doi:10.1016/S0893-9659(99)00126-3.10.1016/S0893-9659(99)00126-3 Search in Google Scholar

[6] DIBLÍK, J.—RŮŽIČKOVÁ, M.—SCHMEIDEL, E.: Asymptotically periodic solutions of Volterra difference equations Tatra Mt. Math. Publ. (43) (2009), 51–61, doi:10.2478/v10127-009-0024-7.10.2478/v10127-009-0024-7 Search in Google Scholar

[7] DIBLÍK, J.—RŮŽIČKOVÁ, M.—SCHMEIDEL E.: Asymptotically periodic solutions of Volterra systems of difference equations, Comput. Math. Appl.59 (2010), no. 8, 2854–2867, doi:10.1016/j.camwa.2010.01.055.10.1016/j.camwa.2010.01.055 Search in Google Scholar

[8] DIBLÍK, J.—RŮŽIČKOVÁ, M.—SCHMEIDEL, E.—ZBASZYNIAK, M.: Weighted asymptotically periodic solutions of linear Volterra difference equations, Abstr. Appl. Anal. 2011 (ID 37098): 1–14, doi10.1155/2011/370982. Search in Google Scholar

[9] ELAYDI, S.: Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl. 181 (1994), no. 2, 483–492, doi:10.1006/jmaa.1994.1037.10.1006/jmaa.1994.1037 Search in Google Scholar

[10] FURUMOCHI, T.: Periodic solutions of Volterra difference equations and attractivity, Nonlinear Anal. (47)(2001), no. 6, 4013–4024, doi:10.1016/S0362-546X(01)00520-X.10.1016/S0362-546X(01)00520-X Search in Google Scholar

[11] JANKOWSKI, R.—SCHMEIDEL, E.: Stability by fixed point theory for functional differential equations, Int. J. Difference Equ. 9 (2014) no.i, 77–86. Search in Google Scholar

[12] JANKOWSKI, R.—SCHMEIDEL, E.: Asymptotically zero solution of a class of higher-nonlinear neutral difference equations with quasidifferences, Discrete Contin. Dyn. Syst. (B), 19 (2014), no. 8, 2691–2696, doi:10.3934/dcdsb.2014.19.2691.10.3934/dcdsb.2014.19.2691 Search in Google Scholar

[13] KOLMANOVSKI, V.—MYSHKIS, A.: Introduction to the Theory and Applications of Functional Differential Equations. Kluwer, Dordrecht, 1999.10.1007/978-94-017-1965-0 Search in Google Scholar

[14] KOSMALA, W.—KULENOVlĆ, M.—LADAS, G.—TEIXEIRAI, C.: On the recursive sequence yn+1=p+yn1qyn+yn1 \[{y_{n + 1}} = \frac{{p + {y_{n - 1}}}}{{q{y_n} + {y_{n - 1}}}}\] , J. Math. Anal. Appl. 251 (2000), no. 2, 571–586, doi:10.1006/jmaa.2000.7032.10.1006/jmaa.2000.7032 Search in Google Scholar

[15] MIGDA, M.—ZHANG, G.: Monotone solutions of neutral difference equations of odd order, J. Difference Equ. Appl. 10 (2007), no. 7, 691–703, doi:10.1080/10236190410001702490.10.1080/10236190410001702490 Search in Google Scholar

[16] MIGDA, M.—SCHMEIDEL, E. —ZDANOWICZ, M.: Asymptotically zero solution of a class of higher nonlinear neutral difference equations with quasidifferences, Appl. Anal. Discrete Math. 9 (2015), no. 2, 271–284, doi:10.2298/AADM150811016M.10.2298/AADM150811016M Search in Google Scholar

[17] MIGDA, M.—SCHMEIDEL, E.—ZDANOWICZ, M.: Boundedness of k-dimensional system of nonlinear difference equations of neutral type, Electron. J. Qual. Theory Differ. Equ. 80 (2015), 1–17, doi:10.14232/ejqtde.2015.1.80.10.14232/ejqtde.2015.1.80 Search in Google Scholar

[18] MYSCHKIS, A.D.: Lineare Differentialgleichungen mit Nacheilendem Argument. VEB Deutscher Verlag der Wissenschaften, Berlin, 1955. Search in Google Scholar

[19] NALINI, S.—BANU, S. M.: New approach to periodicity of neutral type delay difference equations, Appl. Math. Sci. 48 (2015), no. 9, 2371–2379, doi:10.12988/ams.2015.53218.10.12988/ams.2015.53218 Search in Google Scholar

[20] PARHI, N.—TRIPATHY, A.K.: Oscillation of a class of nonlinear neutral difference equations of higher order, J. Math. Anal. Appl. 284 (2003), no. 2, 756–774, 2003. doi:10.1016/S0022-247X(03)00298-1.10.1016/S0022-247X(03)00298-1 Search in Google Scholar

[21] PHILOS, C. G.—PURNARAS, I. K.: The behaviour of the solutions of periodic linear neutral delay difference equations, J. Comput. Appl. Math. 175 (2005), no. 2, 209–230, doi:10.1016/j.cam.2004.05.020.10.1016/j.cam.2004.05.020 Search in Google Scholar

[22] REN, J.—SIEGMUND, S.—HAN, W.: Positive Periodic Solutions for Neutral Difference Equations with Variable Delay. ResearchGate, 2014. https://www.researchgate.net/publication/259574530 Search in Google Scholar

[23] SHARMA, S.: Metric Space. Discovery Publishing Pvt. Ltd, New Delhi, India, 1th edition, 2011. Search in Google Scholar

[24] THANDAPANI, E.—KARUNAKARAN, R.—AROCKIASAMY, I.: Bounded nonoscillatory solutions of neutral type difference systems, J. Qual. Theory Differ Equ. 25 (2009), 1–8, 2009. doi:10.14232/ejqtde.2009.4.25.10.14232/ejqtde.2009.4.25 Search in Google Scholar

[25] WANG, W.—YANG, X.: Positive periodic solutions for neutral functional difference equations, Int. J. Difference Equ. 7 (2012), no. 1, 99–109. Search in Google Scholar

[26] WANG, Z.—SUN, J.: Asymptotic behavior of solutions of nonlinear higher-order neutral type difference equations, J. Difference Equ. Appl. 12 (2006), no. 5, 419–432, doi:10.1080/10236190500539352.10.1080/10236190500539352 Search in Google Scholar

[27] ZHOU, Y.—HUANG, Y. Q.: Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations. J. Math. Anal. Appl. 280 (2003), no. 1, 63–76, doi:10.1016/S0022-247X(03)00017-9.10.1016/S0022-247X(03)00017-9 Search in Google Scholar

[28] ZHOU, Y.—ZHANG, B. G.: Existence of nonoscillatory solutions of higher-order neutral delay difference equations with variable coefficients, Comput. Math. Appl. 45 (2003), no. 6, 991–1000, doi:10.1016/S0898-1221(03)00074-9.10.1016/S0898-1221(03)00074-9 Search in Google Scholar

eISSN:
1338-9750
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
3 Hefte pro Jahr
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines