Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

Open access

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.

References

  • [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.

Journal Information


Mathematical Citation Quotient (MCQ) 2016: 0.28

Target Group

researchers in the fields of: algebraic structures, calculus of variations, combinatorics, control and optimization, cryptography, differential equations, differential geometry, fuzzy logic and fuzzy set theory, global analysis, mathematical physics and number theory

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 19 19 19
PDF Downloads 9 9 9