Oscillatory and asymptotic behavior of a homogeneous neutral delay difference equation of second order
by R. N. Rath   Seshadev Padhi   B. L. Barik  

Vol. 3 No. 3 (2008) P.453~P.467

ABSTRACT

In this paper we find sufficient conditions for every solution of the neutral delay difference equation
$\Delta(r_n\Delta(y_n - p_ny_n - m))+ q_nG(y_{n-k}) = 0$
to oscillate or to tend to zero or $\pm\infty$ as $n \to \infty$, where $\Delta$
is the forward difference operator given by
$\Delta x_n = x_{n+1}- x_n, p_n, q_n,$ and $r_n$ are infinite sequences of real numbers with $q_n \ge 0, r_n > 0$. Different ranges of {$p_n$} are considered. This paper improves, generalizes and corrects some recent results of [1, 9, 12, 13, 14].

KEYWORDS
Oscillatory solution, nonoscillatory solution, asymptotic behaviour, difference equation

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 39A10, 39A12

MILESTONES

Received: 2005-04-16
Revised : 2007-08-11
Accepted: 2007-08-11

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