2019
DOI: 10.1002/mma.6165
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Oscillation of first‐order dynamic equations with nonmonotone delay

Abstract: 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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Cited by 4 publications
(5 citation statements)
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“…then all solutions of (1.5) are oscillatory, while, in 2020, the present author [16] proved that, if…”
Section: Introductionmentioning
confidence: 62%
“…then all solutions of (1.5) are oscillatory, while, in 2020, the present author [16] proved that, if…”
Section: Introductionmentioning
confidence: 62%
“…where ϑ(ζ) is defined by (1.4), then all solutions of (1.3) oscillate. In 2020, Öcalan [17] obtained the following criteria. If −r ∈ R + and…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, there has been much research activity concerning the oscillation and non-oscillation of solutions of delay differential and difference equations. For these oscillatory and non-oscillatory results, we refer, for instance [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”
Section: Introductionmentioning
confidence: 99%
“…In [16], Öcalan proved that if is not necessarily monotone and then all solutions of (1.1) oscillate. It can be seen immediately that if is non-decreasing, then condition (1.20) returns to condition (1.15).…”
Section: Introductionmentioning
confidence: 99%