Green's function and comparison principles for first order periodic differential equations with piecewise constant arguments

Journal of Mathematical Analysis and Applications

Volumn 291, Issue 2, 2004, Pages 690-697

  Cabada, Alberto ^a   Ferreiro, Juan B ^a   Nieto, Juan J ^a  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Comparison results; Green's function; Periodic solutions; Piecewise constant argument

Indexed keywords

EID: 1542406442     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.11.022     Document Type: Article

References (13)

1. S. Busenberg, K. Cooke, Vertically Transmitted Diseases. Models and Dynamics, in: Biomathematics, vol. 23, Springer-Verlag, Berlin, 1993.
2. A. Cabada, The method of lower and upper solutions for second, third, fourth and higher order boundary value problems, J. Math. Anal. Appl. 185 (1994) 302-320.
3. K. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297.
4. K. Cooke, J. Wiener, A survey of differential equations with piecewise continuous arguments, in: Delay Differential Equations and Dynamical Systems, 1990, pp. 1-15.
5. J. Gouzé, T. Sari, A class of piecewise linear differential equations arising in biological models, Special issue: Non-smooth dynamical systems, theory and applications, Dynam. Systems 17 (2002) 299-316.
6. T. Küpper, R. Yuang, On quasi-periodic solutions of differential equations with piecewise constant argument, J. Math. Anal. Appl. 267 (2002) 173-193.
7. J.J. Nieto, A comparison result for a linear differential equation with piecewise constant delay, Glas. Mat. Ser. III 39 (2003) 73-76.
8. S. Sadahisa, H. Tadayuki, Dynamics of a linear differential system with piecewise constant argument, Dynam. Contin. Discrete Impuls. Systems 7 (2000) 585-594.
9. S.M. Shah, J. Wiener, Advanced differential equations with piecewise constant argument deviations, Internat. J. Math. Math. Sci. 6 (1983) 671-703.
10. J. Wiener, Generalized Solutions of Functional-Differential Equations, World Scientific, River Edge, NJ, 1993.
11. J. Wiener, V. Lakshmikantham, A damped oscillator with piecewise constant time delay, Nonlinear Stud. 7 (2000) 78-84.
12. J. Wiener, V. Lakshmikantham, Differential equations with piecewise constant argument and impulsive equations, Nonlinear Stud. 7 (2000) 60-69.
13. F. Zhang, A. Zhao, J. Yan, Monotone iterative method for differential equations with piecewise constant arguments, Portugal. Math. 57 (2000) 345-353.