Nasze serwisy używają informacji zapisanych w plikach cookies. Korzystając z serwisu wyrażasz zgodę na używanie plików cookies zgodnie z aktualnymi ustawieniami przeglądarki, które możesz zmienić w dowolnej chwili. Więcej informacji odnośnie plików cookies.

Obowiązek informacyjny wynikający z Ustawy z dnia 16 listopada 2012 r. o zmianie ustawy – Prawo telekomunikacyjne oraz niektórych innych ustaw.

Wyłącz komunikat

 
 

Logowanie

Logowanie za pomocą Centralnej Usługi Uwierzytelniania PRz. Po zakończeniu pracy nie zapomnij zamknąć przeglądarki.

Journal of Mathematics and Applications

Journal of Mathematics and Applications
04/40, DOI: 10.7862/rf.2017.4

Oscillation of Second Order Difference Equation with a Sub-linear Neutral Term

C. Dharuman, John R. Graef, E. Thandapani, K.S. Vidhyaa

DOI: 10.7862/rf.2017.4

Abstract

This paper deals with the oscillation of a certain class of second order di erence 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.

Full text (pdf)

References

  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 sufficient 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 difference 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 nonlinear difference equations with nonlinear neutral term, Comput. Math. Appl. 41 (2001) 1487-1494.

About this Article

TITLE:
Oscillation of Second Order Difference Equation with a Sub-linear Neutral Term

AUTHORS:
C. Dharuman (1)
John R. Graef (2)
E. Thandapani (3)
K.S. Vidhyaa (4)

AUTHORS AFFILIATIONS:
(1) Department of Mathematics, SRM University, India
(2) Department of Mathematics, University of Tennessee at Chattanooga, USA
(3) Ramanujan Institute for Advanced Study in Mathematics, University of Madras, India
(4) Department of Mathematics, SRM University, India

JOURNAL:
Journal of Mathematics and Applications
04/40

KEY WORDS AND PHRASES:
Difference equations; Oscillation; Sub-linear neutral term; Second order

FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/63

DOI:
10.7862/rf.2017.4

URL:
http://dx.doi.org/10.7862/rf.2017.4

COPYRIGHT:
Publishing House of Rzeszow University of Technology Powstańców Warszawy 12, 35-959 Rzeszow

POLITECHNIKA RZESZOWSKA im. Ignacego Łukasiewicza; al. Powstańców Warszawy 12, 35-959 Rzeszów
tel.: +48 17 865 11 00, fax.: +48 17 854 12 60
Administrator serwisu:

Deklaracja dostępności | Polityka prywatności