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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.21 no.1 Antofagasta May 2002

http://dx.doi.org/10.4067/S0716-09172002000100002 

Proyecciones
Vol. 21, N o 1, pp. 9-19, May 2002.
Universidad Católica del Norte
Antofagasta - Chile

 

ASYMPTOTIC EQUILIBRIUM FOR
CERTAIN TYPE OF DIFFERENTIAL
EQUATIONS WITH MAXIMUM *

 

PATRICIO GONZÁLEZ
Universidad Arturo Prat - Chile

and

MANUEL PINTO
Universidad de Chile - Chile

 

Abstract

In this work we obtain asymptotic representations for the solutions of certain type of differential equations with maxi-mum.We deduce the asymptotic equilibrium for this class of differential equations.

1991 Math. Subject Classification: 34A20

Keywords: Differential equations with maximum, asymptotic representation, asymptotic equilibrium, Banach fixed point the-orem.

3. References

[1] N. R. Bantsur and E. P Trofimchuk, Existence and stability of the periodic and almost periodic solutions of quasilinear systems with maxima. Ukrain. Math. J. 6, pp. 747 - 754, (1998).        [ Links ]

[2] D. D. Bainov and N. G. Kazakova, A finite difference method for solving the periodic problem for autonomous differential equations with maxima, Math. J. Toyama Univ., 15, pp. 1-13, (1992).        [ Links ]

[3] V. H. Cortés and P. González, Levinson’s theorem for impulsive differential equations, Analysis 14, pp. 113-125, (1994).        [ Links ]

[4] P. González and M. Pinto, Stability Properties of the Solutions of the Nonlinear Functional Differential Systems. J. Math. Anal. Appl. Vol. 181, 2, pp. 562-573, (1994).        [ Links ]

[5] P. González and M. Pinto, Asymptotic behavior of impulsive differential equations, Rocky Mountain Journal of Mathematics, 26, pp. 165 - 173, (1996).        [ Links ]

[6] P. González and M. Pinto, Asymptotic behavior of the solutions of certain complex differential equations, Differential Equations and Dinamical Systems, 5, pp. 13 - 23, (1997).        [ Links ]

[7] J. Guzman and M. Pinto, Global existence and asymptotic behavior of solutions of nonlinear differential equations, J, Math. Anal. Appl. 186, pp. 596 - 604, (1994).        [ Links ]

[8] A. D. Myshkis, On some problems of the theory of differential equations with deviating argument, Russ. Math. Surv. 32 (2), pp. 181 - 210, (1977).        [ Links ]

[9] M. Pinto, Asymptotic Integration of System Resulting from a Perturbation of an h-system, J. Math. Anal. Appl. 131, pp.144-216, (1988).        [ Links ]

[10] M. Pinto, Impulsive Inequalities of Bihari Type. Libertas Math 12, pp. 57-70, (1993).        [ Links ]

[11] A. M. Samoilenko, E. P. Trofimchuk and N. R. Bantsur, Peri-odic and almost periodic solutions of the systems of differential equations with maxima. Proc. NAS Ukraine, pp. 53 - 57 (in Ukrainian), (1998).        [ Links ]

Received : December 2001.

Patricio González
Departamento de Ciencias Físicas y Matemáticas
Universidad Arturo Prat
Avenida Arturo Prat 2120
Casilla 121
Iquique
Chile
email: pgonz@cavancha.cec.unap.cl

and

Manuel Pinto
Departamento de Matemáticas
Facultad de Ciencias
Universidad de Chile
Casilla 653
Santiago
Chile
email : pintoj@uchile.cl


*This research was supported by FONDECYT Grant # 8990013

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