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Publication Cover
Applicable Analysis
An International Journal
Volume 23, 1986 - Issue 3
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Original Articles

Oscillatory and periodic solutions of an equation alternately of retarded and advanced type

A. R. Aftabizadeh Department of Mathematics, Ohio University, Athens, OH, 45701
&
Joseph Wiener Department of Mathematics, Pan American University, Edinburg, Texas, 78539
Pages 219-231 | Received 25 Jun 1986, Published online: 02 May 2007

Citations (21)

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Read on this site (2)

D. A. Georgiou, G. Ladas & P. N. Vlahos. (1992) Oscillation and asymptotic behavior of a system of linear difference equations. Applicable Analysis 46:3-4, pages 241-248.
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A.R. Ftabizadeh & Joseph Wiener. (1988) Oscillatory and periodic solutions for systems of two first order linear differential equations with piecewise constant argument. Applicable Analysis 26:4, pages 327-333.
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Articles from other publishers (19)

Yongtang Chen & Qi Wang. (2023) Convergence and stability of Galerkin finite element method for hyperbolic partial differential equation with piecewise continuous arguments. Numerical Methods for Partial Differential Equations 39:5, pages 3754-3776.
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Musa Emre Kavgaci, Huda Al Obaidi & Huseyin Bereketoglu. (2023) Some results on a first-order neutral differential equation with piecewise constant mixed arguments. Periodica Mathematica Hungarica.
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Yongtang Chen & Qi Wang. (2022) Convergence and stability of spectral collocation method for hyperbolic partial differential equation with piecewise continuous arguments. Computational and Applied Mathematics 41:8.
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Kuo-Shou Chiu. (2020) Green’s Function for Periodic Solutions in Alternately Advanced and Delayed Differential Systems. Acta Mathematicae Applicatae Sinica, English Series 36:4, pages 936-951.
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Kuo‐Shou Chiu & Tongxing Li. (2019) Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments. Mathematische Nachrichten 292:10, pages 2153-2164.
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Kuo-Shou Chiu. (2014) Periodic Solutions for Nonlinear Integro-Differential Systems with Piecewise Constant Argument. The Scientific World Journal 2014, pages 1-14.
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Kuo-Shou Chiu & Manuel Pinto. (2011) Variation of parameters formula and Gronwall inequality for differential equations with a general piecewise constant argument. Acta Mathematicae Applicatae Sinica, English Series 27:4, pages 561-568.
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YONGKUN LI & ERLIANG XU. (2010) THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES. Glasgow Mathematical Journal 53:2, pages 369-377.
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Qi Wang, Qingyong Zhu & Mingzhu Liu. (2011) Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type. Journal of Computational and Applied Mathematics 235:5, pages 1542-1552.
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Z.W. Yang, M.Z. Liu & Juan J. Nieto. (2009) Runge–Kutta methods for first-order periodic boundary value differential equations with piecewise constant arguments. Journal of Computational and Applied Mathematics 233:4, pages 990-1004.
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Gen-qiang Wang & Sui Sun Cheng. (2009) Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument. International Journal of Mathematics and Mathematical Sciences 2009, pages 1-14.
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W.J. Lv, Z.W. Yang & M.Z. Liu. (2007) Stability of Runge–Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments. Computers & Mathematics with Applications 54:3, pages 326-335.
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Gen-qiang Wang & Sui Sun Cheng. (2005) Existence of Periodic Solutions for a Neutral Differential Equation with Piecewise Constant Argument. Funkcialaj Ekvacioj 48:2, pages 299-311.
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S. R. Grace, M. R. S. Kulenović & H. El-Metwally. (2002) On the stability of solutions of certain systems of differential equations with piecewise constant argument. Czechoslovak Mathematical Journal 52:3, pages 449-461.
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I.W Rodrigues. (1997) Systems of Differential Equations of Alternately Retarded and Advanced Type. Journal of Mathematical Analysis and Applications 209:1, pages 180-190.
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Kenneth L. Cooke & Joseph Wiener. 1991. Delay Differential Equations and Dynamical Systems. Delay Differential Equations and Dynamical Systems 1 15 .
Yong Kang Huang. (1990) Oscillations and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument. Journal of Mathematical Analysis and Applications 149:1, pages 70-85.
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Joseph Wiener & Kenneth L Cooke. (1989) Oscillations in systems of differential equations with piecewise constant argument. Journal of Mathematical Analysis and Applications 137:1, pages 221-239.
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A.R. Aftabizadeh & Joseph Wiener. (1987) Differential inequalities for delay differential equations with piecewise constant argument. Applied Mathematics and Computation 24:3, pages 183-194.
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