{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T14:24:44Z","timestamp":1773066284507,"version":"3.50.1"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s10998-021-00421-x","type":"journal-article","created":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T18:35:47Z","timestamp":1629484547000},"page":"109-127","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["On a solvable system of p difference equations of higher order"],"prefix":"10.1007","volume":"85","author":[{"given":"Yacine","family":"Halim","sequence":"first","affiliation":[]},{"given":"Amira","family":"Khelifa","sequence":"additional","affiliation":[]},{"given":"Messaoud","family":"Berkal","sequence":"additional","affiliation":[]},{"given":"Abderrahmane","family":"Bouchair","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,20]]},"reference":[{"issue":"2","key":"421_CR1","doi-asserted-by":"publisher","first-page":"701","DOI":"10.18514\/MMN.2019.2923","volume":"20","author":"Y Akrour","year":"2019","unstructured":"Y. Akrour, N. Touafek, Y. Halim, On a system of difference equations of second order solved in closed-form. Miskolc Math. Notes 20(2), 701\u2013717 (2019)","journal-title":"Miskolc Math. Notes"},{"key":"421_CR2","volume-title":"An Introduction to Difference Equations","author":"S Elaydi","year":"1995","unstructured":"S. Elaydi, An Introduction to Difference Equations (Springer, New York, 1995)"},{"key":"421_CR3","first-page":"353","volume":"18","author":"EM Elsayed","year":"2015","unstructured":"E.M. Elsayed, On a system of two nonlinear difference equations of order two. Proc. Jangjeon Math. Soc. 18, 353\u2013368 (2015)","journal-title":"Proc. Jangjeon Math. Soc."},{"issue":"1","key":"421_CR4","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1016\/j.mcm.2011.08.012","volume":"55","author":"EM Elsayed","year":"2012","unstructured":"E.M. Elsayed, Solutions of rational difference systems of order two. Math. Comput. Model. 55(1), 378\u2013384 (2012)","journal-title":"Math. Comput. Model."},{"key":"421_CR5","first-page":"1361","volume":"44","author":"EM Elsayed","year":"2015","unstructured":"E.M. Elsayed, T.F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations. Hacet. J. Math. Stat. 44, 1361\u20131390 (2015)","journal-title":"Hacet. J. Math. Stat."},{"key":"421_CR6","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1007\/s40314-013-0092-9","volume":"33","author":"EM Elsayed","year":"2014","unstructured":"E.M. Elsayed, Solution for systems of difference equations of rational form of order two. Comput. Appl. Math. 33, 751\u2013765 (2014)","journal-title":"Comput. Appl. Math."},{"key":"421_CR7","doi-asserted-by":"publisher","first-page":"976","DOI":"10.1080\/10236198.2018.1443445","volume":"24","author":"M G\u00fcm\u00fcs","year":"2018","unstructured":"M. G\u00fcm\u00fcs, The global asymptotic stability of a system of difference equations. J. Differ. Equ. Appl. 24, 976\u2013991 (2018)","journal-title":"J. Differ. Equ. Appl."},{"key":"421_CR8","first-page":"109","volume":"8","author":"M G\u00fcm\u00fcs","year":"2020","unstructured":"M. G\u00fcm\u00fcs, Analysis of periodicity for a new class of non-linear difference equations by using a new method. Electron. J. Math. Anal. Appl. 8, 109\u2013116 (2020)","journal-title":"Electron. J. Math. Anal. Appl."},{"issue":"2","key":"421_CR9","doi-asserted-by":"publisher","first-page":"1112","DOI":"10.1002\/mma.5915","volume":"43","author":"M G\u00fcm\u00fcs","year":"2020","unstructured":"M. G\u00fcm\u00fcs, The periodic character in a higher order difference equation with delays. Math. Methods Appl. Sci. 43(2), 1112\u20131123 (2020)","journal-title":"Math. Methods Appl. Sci."},{"key":"421_CR10","first-page":"204","volume":"3","author":"Y Halim","year":"2015","unstructured":"Y. Halim, Global character of systems of rational difference equations. Electron. J. Math. Anal. Appl. 3, 204\u2013214 (2015)","journal-title":"Electron. J. Math. Anal. Appl."},{"key":"421_CR11","doi-asserted-by":"publisher","first-page":"79","DOI":"10.18576\/msl\/050111","volume":"5","author":"Y Halim","year":"2016","unstructured":"Y. Halim, Form and periodicity of solutions of some systems of higher-order difference equations. Math. Sci. Lett. 5, 79\u201384 (2016)","journal-title":"Math. Sci. Lett."},{"key":"421_CR12","first-page":"65","volume":"11","author":"Y Halim","year":"2016","unstructured":"Y. Halim, A system of difference equations with solutions associated to Fibonacci numbers. Int. J. Differ. Equ. 11, 65\u201377 (2016)","journal-title":"Int. J. Differ. Equ."},{"key":"421_CR13","doi-asserted-by":"publisher","first-page":"1004","DOI":"10.3906\/mat-1503-80","volume":"39","author":"Y Halim","year":"2015","unstructured":"Y. Halim, N. Touafek, Y. Yazlik, Dynamic behavior of a second-order nonlinear rational difference equation. Turk. J. Math. 39, 1004\u20131018 (2015)","journal-title":"Turk. J. Math."},{"key":"421_CR14","doi-asserted-by":"publisher","first-page":"2974","DOI":"10.1002\/mma.3745","volume":"39","author":"Y Halim","year":"2016","unstructured":"Y. Halim, M. Bayram, On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences. Math. Methods Appl. Sci. 39, 2974\u20132982 (2016)","journal-title":"Math. Methods Appl. Sci."},{"key":"421_CR15","first-page":"166","volume":"5","author":"Y Halim","year":"2017","unstructured":"Y. Halim, J.T.F. Rabago, On some solvable systems of difference equations with solutions associated to Fibonacci numbers. Electron. J. Math. Anal. Appl. 5, 166\u2013178 (2017)","journal-title":"Electron. J. Math. Anal. Appl."},{"issue":"3","key":"421_CR16","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1515\/ms-2017-0130","volume":"68","author":"Y Halim","year":"2018","unstructured":"Y. Halim, J.F.T. Rabago, On the solutions of a second-order difference equations in terms of generalized Padovan sequences. Math. Slovaca 68(3), 625\u2013638 (2018)","journal-title":"Math. Slovaca"},{"issue":"3","key":"421_CR17","doi-asserted-by":"publisher","first-page":"1533","DOI":"10.3906\/mat-1902-24","volume":"43","author":"M Kara","year":"2019","unstructured":"M. Kara, Y. Yazlik, Solvability of a system of nonlinear difference equations of higher order. Turk. J. Math. 43(3), 1533\u20131565 (2019)","journal-title":"Turk. J. Math."},{"issue":"1","key":"421_CR18","first-page":"41","volume":"14","author":"M Kara","year":"2020","unstructured":"M. Kara, Y. Yazlik, On the system of difference equations $$x_{n}=\\frac{x_{n-2}y_{n-3}}{y_{n-1}(a_{n}+b_{n}x_{n-2}y_{n-3})}, y_{n}=\\frac{y_{n-2}x_{n-3}}{x_{n-1}(\\alpha _{n}+\\beta _{n}y_{n-2}x_{n-3})}$$. J. Math. Ext. 14(1), 41\u201359 (2020)","journal-title":"J. Math. Ext."},{"key":"421_CR19","doi-asserted-by":"crossref","unstructured":"M. Kara, Y. Yazlik, D.T. Tollu, Solvability of a system of higher order nonlinear difference equations. Hacet. J. Math. Stat. 49(5), 1566\u20131593 (2020)","DOI":"10.15672\/hujms.474649"},{"issue":"4","key":"421_CR20","doi-asserted-by":"crossref","first-page":"202","DOI":"10.32323\/ujma.610399","volume":"2","author":"A Khelifa","year":"2019","unstructured":"A. Khelifa, Y. Halim, M. Berkal, Solutions of a system of two higher-order difference equations in terms of Lucas sequence. Univ. J. Math. Appl. 2(4), 202\u2013211 (2019)","journal-title":"Univ. J. Math. Appl."},{"issue":"3","key":"421_CR21","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1515\/ms-2017-0378","volume":"70","author":"A Khelifa","year":"2020","unstructured":"A. Khelifa, Y. Halim, A. Bouchair, M. Berkal, On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers. Math. Slovaca 70(3), 641\u2013656 (2020)","journal-title":"Math. Slovaca"},{"key":"421_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1703-8","volume-title":"Global Behavior of Nonlinear Difference Equations of Higher Order with Applications","author":"V Kocic","year":"1993","unstructured":"V. Kocic, G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications (Chapman & Hall, London, 1993)"},{"issue":"1","key":"421_CR23","first-page":"121","volume":"24","author":"JTF Rabago","year":"2017","unstructured":"J.T.F. Rabago, Y. Halim, Supplement to the paper of Halim, Touafek and Elsayed: Part I. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 24(1), 121\u2013131 (2017)","journal-title":"Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal."},{"key":"421_CR24","first-page":"7649","volume":"218","author":"S Stevi\u0107","year":"2012","unstructured":"S. Stevi\u0107, On a third-order system of difference equations. Appl. Math. Comput. 218, 7649\u20137654 (2012)","journal-title":"Appl. Math. Comput."},{"issue":"9","key":"421_CR25","first-page":"5010","volume":"218","author":"S Stevi\u0107","year":"2012","unstructured":"S. Stevi\u0107, On some solvable systems of difference equations. Appl. Math. Comput. 218(9), 5010\u20135018 (2012)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"421_CR26","first-page":"80","volume":"4","author":"S Stevic","year":"2004","unstructured":"S. Stevic, More on a rational recurrence relation. Appl. Math. E-Notes 4(1), 80\u201385 (2004)","journal-title":"Appl. Math. E-Notes"},{"key":"421_CR27","first-page":"310","volume":"233","author":"DT Tollu","year":"2014","unstructured":"D.T. Tollu, Y. Yazlik, N. Taskara, On fourteen solvable systems of difference equations. Appl. Math. Comput. 233, 310\u2013319 (2014)","journal-title":"Appl. Math. Comput."},{"key":"421_CR28","first-page":"7","volume":"174","author":"DT Tollu","year":"2013","unstructured":"D.T. Tollu, Y. Yazlik, N. Taskara, On the solutions of two special types of Riccati difference equation via Fibonacci numbers. Adv. Differ. Equ. 174, 7 (2013)","journal-title":"Adv. Differ. Equ."},{"key":"421_CR29","first-page":"303","volume":"9","author":"N Touafek","year":"2014","unstructured":"N. Touafek, On some fractional systems of difference equations. Iran. J. Math. Sci. Inform. 9, 303\u2013305 (2014)","journal-title":"Iran. J. Math. Sci. Inform."},{"key":"421_CR30","first-page":"867","volume":"41","author":"N Touafek","year":"2012","unstructured":"N. Touafek, On a second order rational difference equation. Hacet. J. Math. Stat. 41, 867\u2013874 (2012)","journal-title":"Hacet. J. Math. Stat."},{"key":"421_CR31","doi-asserted-by":"publisher","first-page":"1987","DOI":"10.1016\/j.mcm.2011.11.058","volume":"55","author":"N Touafek","year":"2012","unstructured":"N. Touafek, E.M. Elsayed, On the solutions of systems of rational difference equations. Math. Comput. Model. 55, 1987\u20131997 (2012)","journal-title":"Math. Comput. Model."},{"key":"421_CR32","doi-asserted-by":"publisher","first-page":"15","DOI":"10.4236\/am.2013.412A002","volume":"12","author":"Y Yazlik","year":"2013","unstructured":"Y. Yazlik, D.T. Tollu, N. Taskara, On the solutions of difference equation systems with Padovan numbers. Appl. Math. 12, 15\u201320 (2013)","journal-title":"Appl. Math."},{"issue":"4","key":"421_CR33","first-page":"813","volume":"45","author":"Y Yazlik","year":"2018","unstructured":"Y. Yazlik, D.T. Tollu, N. Taskara, Behaviour of solutions for a system of two higher-order difference equations. J. Sci. Arts 45(4), 813\u2013826 (2018)","journal-title":"J. Sci. Arts"},{"issue":"2","key":"421_CR34","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.31801\/cfsuasmas.548262","volume":"68","author":"Y Yazlik","year":"2019","unstructured":"Y. Yazlik, M. Kara, On a solvable system of difference equations of higher-order with period two coefficients. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68(2), 1675\u20131693 (2019)","journal-title":"Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat."},{"issue":"1","key":"421_CR35","first-page":"29","volume":"7","author":"Y Yazlik","year":"2019","unstructured":"Y. Yazlik, M. Kara, Be\u015finci mertebeden fark denklem sisteminin \u00e7\u00f6z\u00fclebilirli\u011fi \u00fczerine. Eski\u015feh. Tek. \u00dcniv. Bilim Teknol. Derg. B-Teorik Bilimler 7(1), 29\u201345 (2019)","journal-title":"Eski\u015feh. Tek. \u00dcniv. Bilim Teknol. Derg. B-Teorik Bilimler"}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00421-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10998-021-00421-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-021-00421-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,7]],"date-time":"2023-11-07T17:42:59Z","timestamp":1699378979000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10998-021-00421-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,20]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["421"],"URL":"https:\/\/doi.org\/10.1007\/s10998-021-00421-x","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,20]]},"assertion":[{"value":"8 March 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}