Asymptotic equilibrium for certain type of differential equations with maximum

Patricio González, Manuel Pinto

Resumen


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

Palabras clave


Differential equations with maximum; asymptotic representation; asymptotic equilibrium; Banach fixed point theorem; ecuaciones diferenciales con máximo; representación asintótica; equilibrio asintótico; teorema de punto fijo de Banach.

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Referencias


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).

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).

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

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).

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

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).

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).

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

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

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

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




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

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