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Berezansky, L.; Chatzarakis, G. E.; Domoshnitsky, A.; Stavroulakis, I. P.

Oscillations of difference equations with several oscillating coefficients. (English) Zbl 1473.39014

Abstr. Appl. Anal. 2014, Article ID 392097, 9 p. (2014).
Summary: We study the oscillatory behavior of the solutions of the difference equation \(\Delta x(n)+\sum^m_{i=1}p_i(n)x(\tau_i(n))=0\), \(n\in\mathbb N_0\) [\(\nabla x(n)-\sum^m_{i=1}p_i(n)x(\sigma_i(n))=0\), \(n\in\mathbb N\)] where \((p_i(n)), 1\leq i\leq m\) are real sequences with oscillating terms, \(\tau_i(n)\) [\(\sigma_i(n)\)], \(1\leq i\leq m\) are general retarded (advanced) arguments, and \(\Delta\) [\(\nabla\)] denotes the forward (backward) difference operator \(\Delta x(n)=x(n+1)-x(n)\) [\(\nabla x(n)=x(n)-x(n-1)\)]. Examples illustrating the results are also given.

Cited in 4 Documents

MSC:

39A21 Oscillation theory for difference equations

Keywords:

oscillatory behavior; oscillation terms
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\textit{L. Berezansky} et al., Abstr. Appl. Anal. 2014, Article ID 392097, 9 p. (2014; Zbl 1473.39014)
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References:

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