Journal of Applied Mathematics

Convergence and Divergence of the Solutions of a Neutral Difference Equation

G. E. Chatzarakis and G. N. Miliaras

Full-text: Open access

Abstract

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ [ x ( n ) + c x ( τ ( n ) ) ] + p ( n ) x ( σ ( n ) ) = 0 , where τ ( n ) is a general retarded argument, σ ( n ) is a general deviated argument (retarded or advanced), c R , ( p ( n ) ) n 0 is a sequence of positive real numbers such that p ( n ) p , p R + , and Δ denotes the forward difference operator Δ x ( n ) = x ( n + 1 ) - x ( n ) . Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to cc.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 262316, 18 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818651

Digital Object Identifier
doi:10.1155/2011/262316

Mathematical Reviews number (MathSciNet)
MR2846437

Zentralblatt MATH identifier
1235.39005

Citation

Chatzarakis, G. E.; Miliaras, G. N. Convergence and Divergence of the Solutions of a Neutral Difference Equation. J. Appl. Math. 2011 (2011), Article ID 262316, 18 pages. doi:10.1155/2011/262316. https://projecteuclid.org/euclid.jam/1331818651


Export citation