Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument
Abstract
This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.
[1] M. Akhmet: Nonlinear hybrid continuous/discrete-time models.. Springer Science & Business Media (2011).
[2] H. Bereketoglu, G.S. Oztepe: Convergence of the solution of an impulsive differential equation with piecewise constant arguments. Miskolc Math. Notes 14 (2013) 801-815.
[3] H. Bereketoglu, G.S. Oztepe: Asymptotic constancy for impulsive differential equations with piecewise constant argument. Bull. Math. Soc. Sci. Math. Roumanie Tome 57 (2014) 181-192.
[4] H. Bereketoglu, G. Seyhan, A. Ogun: Advanced impulsive differential equations with piecewise constant arguments. Math. Model. Anal 15 (2) (2010) 175-187.
[5] H. Bereketoglu, G. Seyhan, F. Karakoc: On a second order differential equation with piecewise constant mixed arguments. Carpath. J. Math 27 (1) (2011) 1-12.
[6] S. Busenberg, K. Cooke: Vertically Transmitted Diseases, Models and Dynamics. In: Biomathematics. Springer, Berlin (1993) .
[7] C.H. Chen, H.X. Li: Almost automorphy for bounded solutions to second-order neutral differential equations with piecewise constant arguments. Elect. J. Diff. Eq. 140 (2013) 1-16.
[8] J.L. Gouzé, T. Sari: A class of piecewise linear differential equations arising in biological models. Dynamic. Syst. 17 (4) (2002) 299-316.
[9] F. Karakoc, H. Bereketoglu, G. Seyhan: Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument. Acta Appl. Math. 110 (1) (2010) 499-510.
[10] T. Küpper, R. Yuan: On quasi-periodic solutions of differential equations with piecewise constant argument. J. Math. Anal. Appl. 267 (1) (2002) 173-193.
[11] J. Li, J. Shen: Periodic boundary value problems of impulsive differential equations with piecewise constant argument. J. Nat. Sci. Hunan Norm. Univ. 25 (2002) 5-9.
[12] H.X. Li: Almost periodic solutions of second-order neutral delay - differential equations with piecewise constant arguments. J. Math. Anal. Appl. 298 (2) (2004) 693-709.
[13] J.J. Nieto, R.R. Lopez: Green's function for second-order periodic boundary value problems with piecewise constant arguments. J. Math. Anal. Appl. 304 (1) (2005) 33-57.
[14] G.S. Oztepe, H. Bereketoglu: Convergence in an impulsive advanced differential equations with piecewise constant argument. Bull. Math. Anal. Appl. 4 (2012) 57-70.
[15] G. Seifert: Second order scalar functional differential equations with piecewise constant arguments. J. Difference Equ. Appl. 8 (5) (2002) 427-445.
[16] G.Q. Wang, S.S. Cheng: Existence of periodic solutions for second order Rayleigh equations with piecewise constant argument. Turkish J. Math. 30 (1) (2006) 57-74.
[17] J. Wiener: Generalized solutions of functional differential equations. Singapore, World Scientific (1993).
[18] J. Wiener, V. Lakshmikantham: Excitability of a second-order delay differential equation. Nonlinear Anal. 38 (1) (1999) 1-11.
[19] J. Wiener, V. Lakshmikantham: Differential equations with piecewise constant argument and impulsive equations. Nonlinear Studies 7 (1) (2000) 60-69.
[20] R. Yuan: Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument. Nonlinear Anal. 41 (7) (2000) 871-890.
