Oscillation of higher order functional differential equations with an advanced argument

Graef, John R.

doi:10.1016/j.aml.2020.106685

Cited by 3 publications

(1 citation statement)

References 8 publications

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“…If (P 3 ) does not hold, then we say that (1.1) is in canonical form. In recent years, there are many results dealing with the oscillation of (1.1) and its modifications for the delay case, that is, σ(t) ≤ t, see for example [2,4,7,11,12,14], and few results in the case of σ(t) ≥ t, see [1, 3, 5, 6, 8-10, 13-17, 19, 20, 23]. Many authors paid attention to a comparison technique, which is a powerful tool in the theory of oscillation, see, for instance, the papers [11,19,21,24] for more details.…”

Section: Introductionmentioning

confidence: 99%

Oscillation of noncanonical second-order advanced differential equations via canonical transform

Böhner¹,

Vidhyaa²,

THANDAPANİ³

2022

Constructive Mathematical Analysis

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Section: Introductionmentioning

confidence: 99%

Oscillation of noncanonical second-order advanced differential equations via canonical transform

Böhner¹,

Vidhyaa²,

THANDAPANİ³

2022

Constructive Mathematical Analysis

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New Oscillation Criteria for Higher Order Nonlinear Dynamic Equations

Grace,

Chhatria

2024

Differ Equ Dyn Syst

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This paper deals with some new criteria for the oscillation of higher-order nonlinear dynamic equations with mixed deviating arguments. The purpose of the present paper is the linearization of the equation under consideration. Specifically, we will infer the oscillation of the studied equation from its linear form and establish new oscillation criteria by comparing it with first-order equations whose oscillatory behaviour is known. The obtained results are new, improve, and correlate many of the known oscillation criteria appearing in the literature. The results are illustrated by two examples.

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Exponentially decaying solutions for models with delayed and advanced arguments: Nonlinear effects in linear differential equations

Berezansky¹,

Braverman²,

Pinelas³

2023

Proc. Amer. Math. Soc.

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We consider a scalar linear mixed differential equation with several terms, both delayed and advanced arguments and a bounded right-hand side. Assuming that the deviations of the argument are bounded, we present sufficient conditions when there exists a unique bounded solution on the positive half-line. Explicit tests for a bounded solution of a homogeneous equation to decay exponentially are obtained. Existence of exponentially decaying solutions for this class of differential equations is studied for the first time, and we illustrate sharpness of the results with examples. We show that the standard approach when convergence of all solutions is stated does not work for mixed equations; in addition to an exponentially decaying, there may be a growing solution. All the coefficients and the mixed arguments are assumed to be Lebesgue measurable functions, not necessarily continuous. Though the equation is linear, some properties, as well as the methods applied, are more typical for nonlinear models, for example, fixed-point theorems are used in the proofs.

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Oscillation of higher order functional differential equations with an advanced argument

Cited by 3 publications

References 8 publications

Oscillation of noncanonical second-order advanced differential equations via canonical transform

Oscillation of noncanonical second-order advanced differential equations via canonical transform

New Oscillation Criteria for Higher Order Nonlinear Dynamic Equations

Exponentially decaying solutions for models with delayed and advanced arguments: Nonlinear effects in linear differential equations

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