On the convergence of solutions to second-order neutral difference equations

• Autorzy: Migda Małgorzata , Migda Janusz , Zdanowicz Małgorzata

Identyfikatory

DOI

10.7494/OpMath.2019.39.1.61

• Języki publikacji: EN

Abstrakty

EN

A second-order nonlinear neutral difference equation with a quasi-difference is studied. Sufficient conditions are established under which for every real constant there exists a solution of the considered equation convergent to this constant.

Słowa kluczowe

EN

second-order difference equation asymptotic behavior quasi-differences; Krasnoselskii's fixed point theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 1
• Strony: 61--75
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Migda Małgorzata

• Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland

autor

Migda Janusz

• A. Mickiewicz University Umultowska 87, 61-614 Poznań, Poland

autor

Zdanowicz Małgorzata

• University of Białystok Ciołkowskiego IM, 15-245 Białystok, Poland

Bibliografia

• [1] R.P. Agarwal, S.R. Grace, D. O'Regan, Nonoscillatory solutions for discrete equations, Comput. Math. Appl. 45 (2003), 1297-1302.
• [2] A. Bezubik, M. Migda, M. Nockowska-Rosiak, E. Schmeidel, Trichotomy of nonoscillatory solutions to second-order neutral difference equation with quasi-difference, Adv. Difference Equ. 192 (2015), 14 pp.
• [3] A. Drozdowicz, J. Popenda, Asymptotic behavior of solutions of the second order difference equation, Proc. Amer. Math. Soc. 99 (1987) 1, 135-140.
• [4] M. Galewski, E. Schmeidel, On the well posed solutions for nonlinear second order neutral difference equations, Math. Slovac. 66 (2016) 4, 933-944.
• [5] M. Galewski, R. Jankowski, M. Nockowska-Rosiak, E. Schmeidel, On the existence of bounded solutions for nonlinear second order neutral difference equations, Electron. J. Qual. Theory Differ. Equ. 72 (2014), 1-12.
• [6] R. Jankowski, E. Schmeidel, Almost oscillation criteria for second order neutral difference equation with quasidifferences, Int. J. Difference Equ. 9 (2014), 77-86.
• [7] B.S. Lalli, B.G. Zhang, On existence of positive solutions and bounded oscillations of neutral difference equations, J. Math. Anal. Appl. 166 (1992), 272-287.
• [8] Z. Liu, Y. Xu, S.M. Kang, Global solvability for a second order nonlinear neutral delay difference equation, Comput. Math. Appl. 57 (2009) 4, 587-595.
• [9] Z. Liu, M. Jia, S.M. Kang, Y.C. Kwun, Bounded positive solutions for a third order discrete equation, Abst. Appl. Anal. 2012 (2012), Article ID 237036, 12 pp.
• [10] J. Migda, Approximative solutions to difference equations of neutral type, Appl. Math. Comput. 268 (2015), 763-774.
• [11] M. Migda, Asymptotic behaviour of solutions of nonlinear difference equations, Fasc. Math. 31 (2001), 57-63.
• [12] M. Migda, J. Migda, On a class of first order nonlinear difference equations of neutral type, Math. Comput. Modelling 40 (2004), 297-306.
• [13] M. Migda, J. Migda, Asymptotic properties of solutions of second-order neutral difference equations, Nonlinear Anal. 63 (2005), e789-e799.
• [14] M. Migda, E. Schmeidel, M. Zdanowicz, Bounded solutions of k-dimensional system of nonlinear difference equations of neutral type, Electron. J. Qual. Theory Differ. Equ. 80 (2015), 17 pp.
• [15] E. Schmeidel, An application of measures of noncompactness in investigation of boundedness of solutions of second order neutral difference equations, Adv. Difference Equ. 91 (2013), 9 pp.
• [16] E. Schmeidel, Z. Zbąszyniak, An application of Darbo's fixed point theorem in the investigation of periodicity of solutions of difference equations, Comput. Math. Appl. 64 (2012), 2185-2191.
• [17] E. Thandapani, M.M.S. Manuel, J.R. Graef, P.W. Spikes, Monotone properties of certain classes of solutions of second-order difference equations, Comput. Math. Appl. 36 (1998), 291-297.