Classifications of Solutions of Second Order Nonlinear Neutral Delay Difference Equations With Positive and Negative Coefficients
DOI:
https://doi.org/10.5644/SJM.07.1.06Keywords:
Second order, quasilinear, neutral equation, positive and negative coefficientsAbstract
In this paper the authors classified all solutions of the following equation $$ \Delta\Big( a_{n}\Big( \Delta
(x_{n}+c_{n}x_{n-k})\Big) ^{\alpha}\Big
)+p_{n}f(x_{n-l})-q_{n}g(x_{n-m}) = 0$$ into four classes and obtain conditions for the existence/nonexistence of solutions in these classes. Examples are provided to illustrate the results.
2000 Mathematics Subject Classification. 39A11
Downloads
References
R. P. Agarwal, Difference Equations and Inequalities, Second Edition,Marcel Dekker, NewYork, 2000.
R. P. Agarwal, M. Bohner, S. R. Grace and D. O. Regan, Discrete Oscillation Theory, Hindawi Publ. Comp., NewYork, 2005.
R. P. Agarwal, M. M. S. Manuel and E. Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations, Math. Comput. Modelling, 24 (1996), 5–11.
R. P. Agarwal, M. M. S. Manuel and E.Thandapani, Oscillatory and nonoscillatory behavior of second order neutral delay difference equations II, Appl. Math. Lett., 10 (1997), 103–109.
R. P. Agarwal and P. J. Y. Wong, Advanced Topics in Difference Equations, Dordrecht, Kluwer, 1997.
S. Elizabeth, J. R. Graef, P. Sundarum and E. Thandapani, Classifying nonoscillatory solutions and oscillation of neutral difference equations, J. Difference Equ. Appl., 11 (2005), 605–618.
J. Jiang, Oscillation criteria for second order quasilinear neutral delay difference equations, Appl. Math. Comput., 125 (2002), 287–293.
J. Jiang, Oscillation of second order nonlinear neutral delay difference equations, Appl. Math. Comput., 146 (2003), 791–801.
H. A. El - Morshedy, New oscillation criteria for second order linear difference equations with positive and negative coefficients, Comput. Math. Appl., 58 (2009), 1988–1997.
B. Karpuz, O. Ocalan and M. K. Yildiz, Oscillation of a class of difference equations of second order, Math. Comp. Modelling, 49 (2009), 912–917.
E. Thandapani and M. M. S. Manuel, Summable criteria for a classification of solution of linear difference equations, Indian J. Pure Appl. Math., 28 (1997), 53–62.
E. Thandapani and M. M. S. Manuel, On some classes of solutions of a nonlinear second order difference equation, Indian J. Math., 41 (1999), 95–113.
E. Thandapani and M. M. S. Manuel, Asymptotic and oscillatory behavior of second order neutral delay difference equations, Engineering Simulation, 15 (1998), 423–430.
E. Thandapani and P. Mohankumar, Oscillation and nonoscillation of nonlinear neutral delay difference equations, Tamkang J. Math., 38 (2007), 323–333.
E. Thandapani and S. Pandian, Oscillatory and asymptotic behavior of second order functional difference equations, Indian J. Math., 37 (1995), 221–233.
E. Thandapani, S. Pandian and B. S. Lalli, Oscillatory and nonoscillatory behavior of second order functional difference equations, Appl. Math. Comput., 70 (1995), 53–66.
E. Thandapani, K. Thangavelu and E. Chandrasekaran, Oscillatory behaviour of second order neutral difference equations with positive and negative coefficients, Electron J. Differ. Equ., 145 (2009), 1–8.
G. Zhang and Y. Geo, Oscillation Theory of Difference Equations, Publishing House of Higher Education, 2000.
