Oscillation of second order difference equation with a sub-linear neutral term

• Autorzy: Dharuman C. , Graef J. R. , Thandapani E. , Vidhyaa K. S.

Identyfikatory

DOI

10.7862/rf.2017.4

• Języki publikacji: EN

Abstrakty

EN

This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.

Słowa kluczowe

EN

difference equations; oscillation; second orde; sub-linear neutral term

PL

równania różniczkowe; oscylacja; równania drugiego rzędu

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2017
• Tom: Vol. 40
• Strony: 59--67
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Dharuman C.

• Department of Mathematics, SRM University, Ramapuram Campus, Chennai 600 089, India

autor

Graef J. R.

• Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA

autor

Thandapani E.

• Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600 005, India

autor

Vidhyaa K. S.

• Department of Mathematics, SRM University, Ramapuram Campus, Chennai 600 089, India

Bibliografia

• [1] R.P. Agarwal, M. Bohner, S.R. Grace and D. O'Regan, Discrete Oscillation Theory, Hindawi, New York 2005.
• [2] R.P. Agarwal, S.R. Grace and D. O'Regan, Oscillation Theory for Difference and Functional Differential Equations, Kluwer, The Netherlands 2000.
• [3] G.H. Hardy, J E. Littlewood and G. Polya, Inequalities, Cambridge University Press, London 1934.
• [4] X. Liu,Oscillation of solutions of neutral difference equations with a nonlinear term, Comp. Math. Appl. 52 (2006) 439-448.
• [5] E. Thandapani, Z. Liu, R. Arul and P.S. Raja, Oscillation and asymptotic behavior of second order difference equations with nonlinear neutral term, Appl. Math. E-Notes 4 (2004) 59-67.
• [6] E. Thandapani, S. Pandian and R.K. Balasubramanian, Oscillation of solutions of nonlinear neutral difference equations with nonlinear neutral term, Far East J. Appl. Math. 15 (2004) 47-62.
• [7] E. Thandapani, M. Vijaya and T. Li, On the oscillation of third order half-linear neutral type difference equations, Electron. J. Qual. Theory Differ. Equ. 76 (2011) 1-13.
• [8] E. Thandapani, K. Mahalingam, Necessary and suffcient conditions for oscillation of second order neutral difference equation, Tamkang J. Math. 34 (2003) 137-145.
• [9] E. Thandapani, K. Mahalingam and J.R. Graef, Oscillatory and asymptotic behavior of second order neutral type difference equations, Inter. J. Pure Appl. Math. 6 (2003) 217-230.
• [10] J. Yang, X. Guan and W. Liu, Oscillation and asymptotic behavior of second order neutral diffeerence equation, Ann. Diff. Equ. 13 (1997) 94-106.
• [11] M.K. Yildiz, H. Ogurmez, Oscillation results of higher order nonlinear neutral delay difference equations with a nonlinear neutral term, Hacettepe J. Math. Stat. 43 (2014) 809-814.
• [12] Z. Zhang, J. Chen and C. Zhang, Oscillation of solutions for second order non-linear difference equations with nonlinear neutral term, Comput. Math. Appl. 41 (2001) 1487-1494.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).