On the Oscillation of a Third Order Nonlinear Differential Equation with Piecewise Constant Arguments

Bereketoğlu, Hüseyin; Lafci, Mehtap; Oztepe, Gizem S.

doi:10.1007/s00009-017-0923-9

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…where [⋅] denotes the greatest-integer function, was initiated by Shah and Wiener [29] in 1983 and Ladas [22] in 1988. Diverse applications of the DEPCA theory are discussed in [4,15,20,27,28,33,35]. DEPCA usually describe hybrid dynamical systems (a combination of continuous and discrete systems) and so combine properties of both differential and difference equations; see [3].…”

Section: Introductionmentioning

confidence: 99%

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Chiu

2019

Mathematische Nachrichten

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We study scalar advanced and delayed differential equations with piecewise constant generalized arguments, in short DEPCAG of mixed type, that is, the arguments are general step functions. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed. New criteria extend and improve related results reported in the literature. The efficiency of our criteria is illustrated via several numerical examples and simulations.

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Section: Introductionmentioning

confidence: 99%

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Chiu

2019

Mathematische Nachrichten

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“…Since y(t) > 0 for t ≥ 2n, then This contradicts b+c < −ae a /(e a −1). So Inequality (12) has no eventually positive solution.…”

Section: The Oscillation Of Analytic Solutionmentioning

confidence: 99%

“…For another population model with piecewise constant arguments, Muroya [11] constructed new contractivity condition. Bereketoglu et al [12] obtained some conditions that guarantee the c 2018 Asia Pacific Journal of Mathematics oscillation and asymptotic behaviour of the solutions of a third order nonlinear EPCA.…”

Section: Introductionmentioning

confidence: 99%

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

2018

apjm

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The paper focuses on the stability and oscillation of mixed differential equation with piecewise continuous arguments u (t) = au(t) + bu([t]) + cu(2[(t + 1)/2]). The explicit expression of the analytic solution, the conditions of stability and oscillation of the analytic solution are presented by the technique of solving differential equation, the theory of characteristic and the functional differential inequality, respectively. The results extend some existing ones.

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“…In the past three decades, the theory of EPCA has been intensively studied. Some properties such as stability [1], oscillation [2,3], periodicity [4], bifurcation [5] and asymptotic behavior [6] are included. EPCA has been widely found in scientific and engineering applications such as biology, ecology, control science and so on.…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Linear θ-Method For Coupled Differential Equation with One Delay

2019

apjm

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A. The purpose of this paper is to study stability of numerical solutions for a coupled differential equation with piecewise constant arguments with one delay. A sufficient condition such that the equation is asymptotically stable is derived. Moreover, when the linear θ-method is applied to this equation, it is proved that the linear θ-method is asymptotically stable if and only if 1/2 < θ ≤ 1. Some numerical examples to confirm the theoretical results are given.2010 Mathematics Subject Classification. 65L07, 65L20.Key words and phrases. piecewise constant arguments; coupled differential equation; linear θ-method; numerical solution; Stability.where X(t) = (x(t), y(t), z(t)) T , X 0 = (x 0 , y 0 , z 0 ) T and A =      a 0 0 0 c 0 0 0 e      , B =      0 b 0 0 0 d f 0 0      .

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On the Oscillation of a Third Order Nonlinear Differential Equation with Piecewise Constant Arguments

Cited by 7 publications

References 24 publications

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments

Stability and Oscillation of Mixed Differential Equation with Piecewise Continuous Arguments

Stability Analysis of Linear θ-Method For Coupled Differential Equation with One Delay

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