Oscillations caused by several retarded and advanced arguments

Ladas, G.; Stavroulakis, I. P.

doi:10.1016/0022-0396(82)90029-8

Cited by 144 publications

(60 citation statements)

References 2 publications

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“…hich is impossible, because, using (8) and the fact that, if 4AC > 1, A > 0, then the inequality AA2 + C < X has no real solution. Also from (11) and the fact that y(T) = 0, we have (13) y(n) = y(n -1) / ¿>(s)expl / a(r)dr\ ds.…”

Section: '(T) + A(t)y(t) + B(t)y([t-l])=0 Where A(t) and B(t) Are Comentioning

confidence: 99%

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Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument

Aftabizadeh¹,

Wiener²,

Xu³

1987

Proceedings of the American Mathematical Society

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ABSTRACT. Oscillatory and periodic solutions of retarded functional differential equations are investigated.The study concerns equations with piecewise constant arguments which found applications in certain biomédical problems.1. The study of oscillatory solutions of differential equations with deviating arguments has been the subject of many recent investigations.Of particular importance, however, has been the study of oscillations which are caused by the deviating arguments and which do not appear in the corresponding ordinary differential equation, see [1,[4][5][6][7][8][9][10][11]13].In this paper we study oscillatory properties of solutions of the linear delay differential equations with piecewise constant deviating argument of the typewhere a(t) and b(t) are continuous functions on [0, oo), and [•] designates the greatest integer function. Such equations are similar in structure to those found in certain "sequential-continuous" models of disease dynamics as treated by Busenberg and Cooke [2]. We give sufficient condition under which equation (1) has oscillatory solutions. We emphasize the fact that our condition is the "best possible" in the sense that when a and b are constants the condition reduces to b > ae~a/4(ea -1) which is a necessary and sufficient condition. In case of constant coefficients we find conditions under which oscillatory solutions are periodic. As it is customary, a solution is said to be oscillatory if it has arbitrarily large zeros.2. In this section we give a sufficient condition under which equation (1) (iii) equation (1) is satisfied on each interval [n,n+ 1) C [0, oo) with integral endpoints.

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Section: '(T) + A(t)y(t) + B(t)y([t-l])=0 Where A(t) and B(t) Are Comentioning

confidence: 99%

“…Of particular importance, however, has been the study of oscillations which are caused by the deviating arguments and which do not appear in the corresponding ordinary differential equation, see [1,[4][5][6][7][8][9][10][11]13].…”

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confidence: 99%

Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument

Aftabizadeh¹,

Wiener²,

Xu³

1987

Proceedings of the American Mathematical Society

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“…In the same paper, the authors proved that if for some j ∈ N lim sup 18) then all solutions of (E) oscillate. …”

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confidence: 95%

Improved iterative oscillation tests for first-order deviating differential equations

Chatzarakis

Jadlovská

2018

OpMath

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Abstract. In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing lim sup and lim inf on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.

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“…It is interesting to note that any of the nonlinear functions in Eqs. (11)-(13) satisfy conditions (9), (10), and (27) of Theorem 6. Furthermore, our results can be extended to more general equations of the form y(') + L Vjfjiyi1 -tj)) = °> j=i which involve different functions fj each of which satisfies conditions (9), (10), and (27).…”

mentioning

confidence: 95%

“…Another, independent condition which implies that Eq. (15) has no real roots is, for example, which was used in [10]. Furthermore, in Theorem 3 the function / may be the "logistic" function (8), a linear function, any of the nonlinear functions in Eqs.…”

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confidence: 99%

On oscillation of nonlinear delay differential equations

Kulenović¹,

Ladas²,

Meimaridou³

1987

Quart. Appl. Math.

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Abstract. Necessary, sufficient, and necessary and sufficient conditions are obtained for all solutions of the nonlinear differential equation Our results show that for a certain class of nonlinear functions /, (*) oscillates if and only if (**) oscillates. As an application of our results, we obtain simple sufficient and necessary and sufficient conditions for the oscillation of several nonlinear delay differential equations which appear in applications.

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Oscillations caused by several retarded and advanced arguments

Cited by 144 publications

References 2 publications

Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument

Oscillatory and Periodic Solutions of Delay Differential Equations with Piecewise Constant Argument

Improved iterative oscillation tests for first-order deviating differential equations

On oscillation of nonlinear delay differential equations

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