The fixed sign property of solutions and stability of linear differential equations with varying distributed delay

Malygina, V. V.; Sabatulina, T. L.

doi:10.3103/s1066369x08080082

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2010

2022

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Cited by 7 publications

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“…For Eq. (4.2) and its modifications with a variable delay h(t) and also the upper bound τ (t), where h(t) ≤ τ (t) ≤ t sharp oscillation results were recently obtained in [7,8].…”

Section: Discussion and Open Problemsmentioning

confidence: 94%

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Oscillation of equations with an infinite distributed delay

Berezansky

Braverman

2010

Computers & Mathematics with Applications

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a b s t r a c tFor the equation with a finite or infinite distributed delaẏthe existence of nonoscillatory solutions is studied. A general comparison theorem is obtained which allows to compare oscillation properties of equations with concentrated delays to integrodifferential equations. Sharp nonoscillation conditions are deduced for some autonomous integrodifferential equations. Using comparison theorems, an example is constructed where oscillation properties of an integrodifferential equation are compared to equations with several concentrated delay which can be treated as its finite difference approximations.

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“…For Eq. (4.2) and its modifications with a variable delay h(t) and also the upper bound τ (t), where h(t) ≤ τ (t) ≤ t sharp oscillation results were recently obtained in [7,8].…”

Section: Discussion and Open Problemsmentioning

confidence: 94%

“…where R 3 (t, s) = R 1 (t, s) + R 2 (t, s), R 1 , R 2 are defined by (1.4), (1.6), respectively, and a mixed equation with an infinite number of delays: Among numerous publications on the oscillation of equations with a deviating argument we mention here papers [1][2][3][4][5][6][7][8], which are concerned with a distributed delay.…”

Section: Introductionmentioning

confidence: 99%