Classification and existence of nonoscillatory solutions of higher order nonlinear neutral difference equations



In this paper, we consider the higher order nonlinear neutral delay difference equation of the form
$$\Delta ^r (x_n + px_{n - \tau } ) + f(n,x_{n - \sigma _1 (n)} ,x_{n - \sigma _2 (n)} ,...,x_{n - \sigma _m (n)} ) = 0.$$
We give an integrated classification of nonoscillatory solutions of the above equation according to their asymptotic behaviours. Necessary and sufficient conditions for the existence of nonoscillatory solutions with designated asymptotic properties are also established.

AMS Mathematics Subject Classification


Key words and phrases

Nonoscillatory solutions neutral difference equations classification 


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Copyright information

© Korean Society for Computational and Applied Mathematics 2005

Authors and Affiliations

  1. 1.Department of MathematicsXiangtan UniversityHunanP. R. China

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