On a linear delay difference equation with impulses. (English) Zbl 1008.39008

Consider the difference equation with impulses \[ \Delta x(n)+p(n) x(n-k)=0\quad n\in N\text{ and }n\in n_j\quad\Delta x(n_j)=b_jx(n_j)\quad j=1,2,\dots \tag{*} \] where \(\Delta x(n)=x(n+1)-x(n) p(n)\) is a sequence of non-negative real numbers, \(n_j\) is a sequence of non-negative integers with \(n_j<n_{j+1}\) for \(j=1,2,\dots \) and \(n_j\rightarrow \infty\) as \(j\rightarrow \infty\) \(b_j\) is a sequence of real numbers, and \(k\) is a positive integer. The author obtains sufficient conditions for the oscillation of all solutions of (*). These conditions improve previous conditions obtained by G. P. Wei [J. Hunan Univ., Nab. Sci. 26, No. 6, 9-13 (1999; Zbl 0965.39005)].
Reviewer: Fozi Dannan (Doha)


39A11 Stability of difference equations (MSC2000)


Zbl 0965.39005