{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T23:02:43Z","timestamp":1649113363414},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2014,5,15]],"date-time":"2014-05-15T00:00:00Z","timestamp":1400112000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Period Math Hung"],"published-print":{"date-parts":[[2014,6]]},"DOI":"10.1007\/s10998-014-0030-7","type":"journal-article","created":{"date-parts":[[2014,5,14]],"date-time":"2014-05-14T08:45:37Z","timestamp":1400057137000},"page":"193-206","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On stability regions for some delay differential equations and their discretizations"],"prefix":"10.1007","volume":"68","author":[{"given":"Jan","family":"\u010cerm\u00e1k","sequence":"first","affiliation":[]},{"given":"Jana","family":"Hrabalov\u00e1","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,5,15]]},"reference":[{"key":"30_CR1","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780198506546.001.0001","volume-title":"Numerical Methods for Delay Differential Equations, Numerical Mathematics and Scientific Computation","author":"A Bellen","year":"2003","unstructured":"A. Bellen, M. Zennaro, Numerical Methods for Delay Differential Equations, Numerical Mathematics and Scientific Computation (The Clarendon Press, Oxford University Press, New York, 2003)"},{"key":"30_CR2","doi-asserted-by":"crossref","unstructured":"J. \u010cerm\u00e1k, J. J\u00e1nsk\u00fd, P. Kundr\u00e1t, On necessary and sufficient conditions for the asymptotic stability of higher order linear difference equations. J. Differ. Equ. Appl. 18, 1781\u20131800 (2012). doi: 10.1080\/10236198.2011.595406","DOI":"10.1080\/10236198.2011.595406"},{"key":"30_CR3","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/0898-1221(94)00095-6","volume":"28","author":"KL Cooke","year":"1994","unstructured":"K.L. Cooke, I. Gy\u0151ri, Numerical approximation of the solutions of delay-differential equations on an infinite interval using piecewise-constant arguments. Comput. Math. Appl. 28, 81\u201392 (1994)","journal-title":"Comput. Math. Appl."},{"key":"30_CR4","first-page":"423","volume":"6","author":"FM Dannan","year":"2004","unstructured":"F.M. Dannan, S. Elaydi, Asymptotic stability of linear difference equations of advanced type. J. Comput. Anal. Appl. 6, 423\u2013428 (2004)","journal-title":"J. Comput. Anal. Appl."},{"key":"30_CR5","doi-asserted-by":"crossref","first-page":"5391","DOI":"10.1016\/j.amc.2011.11.023","volume":"218","author":"J Dibl\u00edk","year":"2012","unstructured":"J. Dibl\u00edk, M. R\u016f\u017ei\u010dkov\u00e1, Z. \u0160ut\u00e1, Asymptotic convergence of the solutions of a discrete equation with several delays. Appl. Math. Comput. 218, 5391\u20135401 (2012)","journal-title":"Appl. Math. Comput."},{"key":"30_CR6","doi-asserted-by":"crossref","unstructured":"J. Dibl\u00edk and A. Zafer, On stability of linear delay differential equations under Perron\u2019s condition. Abstr. Appl. Anal. 2011 (2011), Article ID 134072","DOI":"10.1155\/2011\/134072"},{"key":"30_CR7","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1093\/imanum\/18.3.399","volume":"18","author":"N Guglielmi","year":"1998","unstructured":"N. Guglielmi, Delay dependent stability regions of $$\\Theta $$ \u0398 -methods for delay differential equations. IMA J. Numer. Anal. 18, 399\u2013418 (1998)","journal-title":"IMA J. Numer. Anal."},{"key":"30_CR8","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1007\/s10998-008-5055-5","volume":"56","author":"I Gy\u0151ri","year":"2008","unstructured":"I. Gy\u0151ri, F. Hartung, On numerical approximation using differential equations with piecewise-constant arguments. Period. Math. Hung. 56, 55\u201369 (2008)","journal-title":"Period. Math. Hung."},{"key":"30_CR9","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1112\/jlms\/s1-25.3.226","volume":"25","author":"ND Hayes","year":"1950","unstructured":"N.D. Hayes, Roots of the transcendental equations associated with certain difference\u2013differential equations. J. Lond. Math. Soc. 25, 226\u2013232 (1950)","journal-title":"J. Lond. Math. Soc."},{"key":"30_CR10","unstructured":"M.M. Kipnis, I.S. Levitskaya, Stability of delay dependent difference and differential equations: similarities and distinctions. in Proceedings of the International Conference on Difference Equations, Special Functions and Orthogonal polynomials, July 25\u201330, Munich (2005), pp. 315\u2013324"},{"key":"30_CR11","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-1965-0","volume-title":"Introduction to the Theory and Applications of Functional Differential Equations","author":"V Kolmanovskii","year":"1999","unstructured":"V. Kolmanovskii, A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations (Kluwer, Dordrecht, 1999)"},{"key":"30_CR12","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1006\/jmaa.1994.1457","volume":"188","author":"SA Kuruklis","year":"1994","unstructured":"S.A. Kuruklis, The asymptotic stability of $$x_{n+1}-a x_n+b x_{n-k}=0$$ x n + 1 - a x n + b x n - k = 0 . J. Math. Anal. Appl. 188, 719\u2013731 (1994)","journal-title":"J. Math. Anal. Appl."},{"key":"30_CR13","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/0040-5809(76)90043-5","volume":"9","author":"SA Levin","year":"1976","unstructured":"S.A. Levin, R. May, A note on difference delay equations. Theor. Popul. Biol. 9, 178\u2013187 (1976)","journal-title":"Theor. Popul. Biol."},{"key":"30_CR14","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1016\/j.jmaa.2004.08.048","volume":"303","author":"E Liz","year":"2005","unstructured":"E. Liz, On explicit conditions for the asymptotic stability of linear higher order difference equations. J. Math. Anal. Appl. 303, 492\u2013498 (2005)","journal-title":"J. Math. Anal. Appl."},{"key":"30_CR15","volume-title":"Geometry of Polynomials","author":"M Marden","year":"1966","unstructured":"M. Marden, Geometry of Polynomials (American Mathematical Society, Providence, 1966)"},{"key":"30_CR16","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10998-008-5097-7","volume":"56","author":"R Medina","year":"2008","unstructured":"R. Medina, M. Pituk, Asymptotic behavior of a linear difference equation with continuous time. Period. Math. Hung. 56, 97\u2013104 (2008)","journal-title":"Period. Math. Hung."}],"container-title":["Periodica Mathematica Hungarica"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-014-0030-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10998-014-0030-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10998-014-0030-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T01:53:04Z","timestamp":1559353984000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10998-014-0030-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5,15]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,6]]}},"alternative-id":["30"],"URL":"https:\/\/doi.org\/10.1007\/s10998-014-0030-7","relation":{},"ISSN":["0031-5303","1588-2829"],"issn-type":[{"value":"0031-5303","type":"print"},{"value":"1588-2829","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5,15]]}}}