Neutral Differential Equations

Agarwal, Ravi P.; Berezansky, Leonid; Braverman, Elena; Domoshnitsky, Alexander

doi:10.1007/978-1-4614-3455-9_6

Cited by 3 publications

(1 citation statement)

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“…As a result of these indispensable generalizations, authors have developed qualitative theories on functional differential equations, we can mention the papers and books in [1,2,3,4,5,6,7,8,9]. In [10], neutral differential equations are classified into two, one of them can be integrated leading to a term with a concentrated delay and an integral term, the second has a derivative involved both without a delay and with one or several delays. The behaviour of solutions of these functional differential equations of the second-, third-and higher order has been intensively investigated and still being under serious investigation in literature.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of solutions to certain nonlinear third order neutral functional differential equation

Ademola

2021

Heliyon

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This paper presents asymptotic behaviour of solution to certain nonlinear nonautonomous neutral functional differential equation of the third order. The third order functional differential equation is cut back to system of first order and used together with a quadratic function to acquire suitable complete Lyapunov-Krasovskii functional. This functional is tested and employed to set up conditions on the nonlinear terms to guarantee stability, asymptotic stability, uniform stability, uniform asymptotic stability of the trivial solution, ultimate boundedness and uniform ultimate boundedness of the nontrivial solutions of the equations under consideration. The results of this paper are new as there are no existing results on the type of equation discussed. Examples are also given to validate the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Asymptotic behaviour of solutions to certain nonlinear third order neutral functional differential equation

Ademola

2021

Heliyon

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Second-order half-linear delay differential equations: Oscillation tests

Bazighifan

Santra²

2020

Advances in the Theory of Nonlinear Analysis and Its Application

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Dierential equations of second-order appear in physical applications such as uid dynamics, electromagnetism, acoustic vibrations and quantum mechanics. In this paper, necessary and sucient conditions are established of the solutions to second-order helf-linear delay dierential equations of the form r(w) µ 1 (ι) + q(ι)w µ (κ(ι)) = 0 , under the assumption ∞ ι r(s) −1/µ 1 ds = ∞. We consider two cases when µ 1 > µ and µ 1 < µ. Some examples are given to show eectiveness and applicability of the main result, and state an open problem.

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