Convergence and Divergence of the Solutions of a Neutral Difference Equation

G. E. Chatzarakis and G. N. Miliaras

Journal of Applied Mathematics, 2011, vol. 2011, 1-18

Abstract:

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ [ ð ‘¥ ( ð ‘› ) + ð ‘ ð ‘¥ ( ð œ ( ð ‘› ) ) ] + ð ‘ ( ð ‘› ) ð ‘¥ ( 𠜎 ( ð ‘› ) ) = 0 , where ð œ ( ð ‘› ) is a general retarded argument, 𠜎 ( ð ‘› ) is a general deviated argument (retarded or advanced), ð ‘ âˆˆ â„ , ( ð ‘ ( ð ‘› ) ) ð ‘› ≥ 0 is a sequence of positive real numbers such that ð ‘ ( ð ‘› ) ≥ ð ‘ , ð ‘ âˆˆ â„ + , and Δ denotes the forward difference operator Δ ð ‘¥ ( ð ‘› ) = ð ‘¥ ( ð ‘› + 1 ) − ð ‘¥ ( ð ‘› ) . Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to ð ‘ .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:262316

DOI: 10.1155/2011/262316

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