Oscillations of difference equations with several oscillating coefficients

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

doi:10.1155/2014/392097

Oscillations of difference equations with several oscillating coefficients

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study the oscillatory behavior of the solutions of the difference equation Δx(n)+i=1mpi(n)x(τi(n))=0,nN0[xn-i=1mpinxσin=0, nN] where (pi(n)), 1≤i≤m are real sequences with oscillating terms, τi(n)[σi(n)], 1≤i≤m are general retarded (advanced) arguments, and Δ[] denotes the forward (backward) difference operator Δx(n)=x(n+1)-x(n)[x(n)=x(n)-x(n-1)]. Examples illustrating the results are also given.

Original language	English
Article number	392097
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.1155/2014/392097
State	Published - 2014

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title = "Oscillations of difference equations with several oscillating coefficients",

abstract = "We study the oscillatory behavior of the solutions of the difference equation Δx(n)+i=1mpi(n)x(τi(n))=0,nN0[xn-i=1mpinxσin=0, nN] where (pi(n)), 1≤i≤m are real sequences with oscillating terms, τi(n)[σi(n)], 1≤i≤m are general retarded (advanced) arguments, and Δ[] denotes the forward (backward) difference operator Δx(n)=x(n+1)-x(n)[x(n)=x(n)-x(n-1)]. Examples illustrating the results are also given.",

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AU - Berezansky, L.

AU - Chatzarakis, G. E.

AU - Domoshnitsky, A.

AU - Stavroulakis, I. P.

PY - 2014

Y1 - 2014

N2 - We study the oscillatory behavior of the solutions of the difference equation Δx(n)+i=1mpi(n)x(τi(n))=0,nN0[xn-i=1mpinxσin=0, nN] where (pi(n)), 1≤i≤m are real sequences with oscillating terms, τi(n)[σi(n)], 1≤i≤m are general retarded (advanced) arguments, and Δ[] denotes the forward (backward) difference operator Δx(n)=x(n+1)-x(n)[x(n)=x(n)-x(n-1)]. Examples illustrating the results are also given.

AB - We study the oscillatory behavior of the solutions of the difference equation Δx(n)+i=1mpi(n)x(τi(n))=0,nN0[xn-i=1mpinxσin=0, nN] where (pi(n)), 1≤i≤m are real sequences with oscillating terms, τi(n)[σi(n)], 1≤i≤m are general retarded (advanced) arguments, and Δ[] denotes the forward (backward) difference operator Δx(n)=x(n+1)-x(n)[x(n)=x(n)-x(n-1)]. Examples illustrating the results are also given.

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JO - Abstract and Applied Analysis

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Oscillations of difference equations with several oscillating coefficients

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