Oscillation criteria of first order linear difference equations with delay argument

Chatzarakis, George E.; Koplatadze, Roman; Stavroulakis, I. P.

doi:10.1016/j.na.2006.11.055

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Oscillation Criteria For (1)4

Theorem I ([8 Theorem 22]) If1

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Cited by 46 publications

(36 citation statements)

References 9 publications

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“…Further, we present some new results that improve the upper limit test Theorem D. Our results improve the results in the papers [1,8,18]. …”

Section: Theorem I ([8 Theorem 22]) Ifsupporting

confidence: 81%

New oscillation tests and some refinements for first-order delay dynamic equations

Öcalan¹

2016

Turk J Math

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“…Further, we present some new results that improve the upper limit test Theorem D. Our results improve the results in the papers [1,8,18]. …”

Section: Theorem I ([8 Theorem 22]) Ifsupporting

confidence: 81%

New oscillation tests and some refinements for first-order delay dynamic equations

Öcalan¹

2016

Turk J Math

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“…In 2008 Chatzarakis et al [7] and in 2008 and 2009 Chatzarakis et al [9,10] derived the following conditions. Theorem 23 (see [7,9,10] …”

Section: Oscillation Criteria For (1)mentioning

confidence: 96%

“…Using the upper bound of the ratio ( ( ))/ ( ) for possible nonoscillatory solutions ( ) of (1) , presented in [7][8][9][10], the above result was essentially improved in 2014 by Stavroulakis [30].…”

Section: Oscillation Criteria For (1)mentioning

confidence: 98%

“…Remark 19 (see [7]). Clearly, the sequence of integers ( ) is nondecreasing and ( ) ≤ ( ) for all ≥ 0.…”

Section: Oscillation Criteria For (1)mentioning

confidence: 99%

“…In 2008, Chatzarakis et al [7] investigated for the first time the oscillatory behavior of equation (1) in the case of a general nonmonotone delay argument ( ) and derived the following theorem.…”

Section: Oscillation Criteria For (1)mentioning

confidence: 99%

See 2 more Smart Citations

Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

Moremedi

Stavroulakis

2018

Discrete Dynamics in Nature and Society

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Consider the first-order delay difference equation with a constant argument Δ ( ) + ( ) ( − ) = 0, = 0, 1, 2, . . . , and the delay difference equation with a variable argument Δ ( ) + ( ) ( ( )) = 0, = 0, 1, 2, . . . , where ( ) is a sequence of nonnegative real numbers, is a positive integer, Δ ( ) = ( + 1) − ( ), and ( ) is a sequence of integers such that ( ) ≤ − 1 for all ≥ 0 and lim →∞ ( ) = ∞. A survey on the oscillation of all solutions to these equations is presented. Examples illustrating the results are given.

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Oscillation of first‐order dynamic equations with nonmonotone delay

Öcalan

2019

Math Meth Appl Sci

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Consider the first‐order dynamic equations xΔ(t)+p(t)xτ(t)=0,t∈[t0,∞)T where p∈Crd()false[t0,∞false)double-struckT,double-struckR+, τ∈Crd()false[t0,∞false)double-struckT,double-struckT and τfalse(tfalse)≤t,1emlimt→∞τfalse(tfalse)=∞. Under the assumption that the τfalse(tfalse) is not necessarily monotone, we present new sufficient conditions for the oscillation of first‐order delay dynamic equations on time scales.

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Oscillation criteria of first order linear difference equations with delay argument

Cited by 46 publications

References 9 publications

New oscillation tests and some refinements for first-order delay dynamic equations

New oscillation tests and some refinements for first-order delay dynamic equations

Oscillation Conditions for Difference Equations with a Monotone or Nonmonotone Argument

Oscillation of first‐order dynamic equations with nonmonotone delay

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