New oscillation conditions for first-order linear retarded difference equations with non-monotone arguments

• Autorzy: Attia Emad R. , El-Matary Bassant M. , Chatzarakis George E.

Identyfikatory

DOI

10.7494/OpMath.2022.42.6.769

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the oscillatory behavior of the solutions of a first-order difference equation with non-monotone retarded argument and nonnegative coefficients, based on an iterative procedure. We establish some oscillation criteria, involving lim sup, which achieve a marked improvement on several known conditions in the literature. Two examples, numerically solved in MAPLE software, are also given to illustrate the applicability and strength of the obtained conditions.

Słowa kluczowe

EN

oscillation; difference equations; non-monotone argument

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 6
• Strony: 769--791
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Attia Emad R.

• Prince Sattam Bin Abdulaziz University, College of Sciences and Humanities in Alkharj, Department of Mathematics, Alkharj 11942, Saudi Arabia
• Damietta University, Faculty of Science, Department of Mathematics, New Damietta 34517, Egypt

• https://orcid.org/0000-0002-7978-5386

autor

El-Matary Bassant M.

• Qassim University, College of Science and Arts, Department of Mathematics, Al-Badaya, Buraidah, Saudi Arabia
• Damietta University, Faculty of Science, Department of Mathematics, New Damietta 34517, Egypt

• https://orcid.org/0000-0003-4525-156X

autor

Chatzarakis George E.

• Department of Electrical and Electronic Engineering Educators, School of Pedagogical and Technological Education (ASPETE), Athens, Marousi 15122, Athens, Greece

• https://orcid.org/0000-0002-0477-1895

Bibliografia

• [1] R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
• [2] E.R. Attia, Oscillation tests for first-order linear differential equations with non-monotone delays, Adv. Difference Equ. 2021 (2021), Article no. 41.
• [3] E.R. Attia, G.E. Chatzarakis, Oscillation tests for difference equations with non-monotone retarded arguments, Appl. Math. Lett. 123 (2022), 107551.
• [4] E.R. Attia, B.M. El-Matary, New aspects for the oscillation of first-order difference equations with deviating arguments, Opuscula Math. 42 (2022), 393–413.
• [5] E. Braverman, B. Karpuz, On oscillation of differential and difference equations with non-monotone delays, Appl. Math. Comput. 218 (2011), 3880–3887.
• [6] E. Braverman, G.E. Chatzarakis, I.P. Stavroulakis, Iterative oscillation tests for difference equations with several non-monotone arguments, J. Differ. Equ. Appl. 21 (2015), 854–874.
• [7] G.E. Chatzarakis, Sufficient oscillation conditions for deviating difference equations, Filomat 33 (2019), 3291–3305.
• [8] G.E. Chatzarakis, I. Jadlovská, Oscillations in deviating difference equations using an iterative technique, J. Inequal. Appl. 2017 (2017), Article no. 173.
• [9] G.E. Chatzarakis, I. Jadlovská, Improved iterative oscillation tests for first-order deviating difference equations, Int. J. Difference Equ. 12 (2017), 185–210.
• [10] G.E. Chatzarakis, I. Jadlovská, Oscillations of deviating difference equations using an iterative method, Mediterr. J. Math. 16 (2019), Article no. 16.
• [11] G.E. Chatzarakis, L. Shaikhet, Oscillation criteria for difference equations with non-monotone arguments, Adv. Difference Equ. 2017 (2017), Article no. 62.
• [12] G.E. Chatzarakis, S.R. Grace, I. Jadlovská, Oscillation tests for linear difference equations with non-monotone arguments, Tatra Mt. Math. Publ. 79 (2021), 81–100.
• [13] G.E. Chatzarakis, R. Koplatadze, I.P. Stavroulakis, Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal. 68 (2008), 994–1005.
• [14] G.E. Chatzarakis, R. Koplatadze, I.P. Stavroulakis, Optimal oscillation criteria of first order linear difference equations with delay argument, Pacific J. Math. 235 (2008), 15–33.
• [15] G.E. Chatzarakis, Ch.G. Philos, I.P. Stavroulakis, On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differential Equations 2008 (2008), no. 50, 1-15.
• [16] G.E. Chatzarakis, Ch.G. Philos, I.P. Stavroulakis, An oscillation criterion for linear difference equations with general delay argument, Port. Math. 66 (2009), 513–533.
• [17] G.E. Chatzarakis, I.K. Purnaras, I.P. Stavroulakis, Oscillation of retarded difference equations with a non-monotone argument, J. Difference Equ. Appl. 23 (2017), 1354–1377.
• [18] L.H. Erbe, B.G. Zhang, Oscillation of discrete analogues of delay equations, Differential Integral Equations 2 (1989), 300–309.
• [19] B. Karpuz, Sharp oscillation and nonoscillation tests for linear difference equations, J. Difference Equ. Appl. 23 (2017), 1929–1942.
• [20] G. Ladas, Ch.G. Philos, Y.G. Sficas, Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation 2 (1989), 101–111.
• [21] J. Shen, I.P. Stavroulakis, Oscillation criteria for delay difference equations, Electron. J. Differential Equations 2001 (2001), 1–15.
• [22] I.P. Stavroulakis, Oscillations of delay difference equations, Comput. Math. Appl. 29 (1995), 83–88.
• [23] I.P. Stavroulakis, Oscillation criteria for first order delay difference equations, Mediterr. J. Math. 1 (2004), 231–240.
• [24] I.P. Stavroulakis, Oscillation criteria for delay and difference equations with non-monotone arguments, Appl. Math. Comput. 226 (2014), 661–672.
• [25] B.G. Zhang, C.J. Tian, Nonexistence and existence of positive solutions for difference equations with unbounded delay, Comput. Math. Appl. 36 (1998), 1–8.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).