# Some existence results for differential equations with both retarded and advanced arguments

## Abstract

Existence, uniqueness an monotone approximation of solutions to the  Cauchy problem for differential equations with both advanced  and retarded arguments are obtained.

## Authors

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

## Keywords

Cauchy problem, fixed points, retarded and advanced arguments.

## Paper coordinates

R. Precup, Some existence results for differential equations with both retarded and advanced arguments, Mathematica (Cluj) 44 (2002). no. 1, pp. 25-31

## About this paper

Mathematica

##### Publisher Name

Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania

##### Online ISSN

google scholar link

[1] Bainov, D. and Mishev, D.P., Oscillation Theory for Neutral Differential Equations with Delay, Adam Hilger, Bristol, 1991.
[2] Elsgolts, L.E. and Norkin, S.B., Introduction to the Theory of Differential Equations with Deviating Arguments (Russian), Nauka, Moscow, 1971.
[3] Gopalsamy, K., Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer, Dordrecht, 1992.
[4] Hale, J., Theory of Functional Differential Equations, Springer-Verlag, Berlin, 1977.
[5] Kolmanovskii, V. and Myshkis, A., Applied Theory of Functional Differential Equations, Kluwer, Dordrecht, 1992.
[6] Kuang, Y., Delay Differential Equations with Applications to Population Dynamics, Academic Press, Boston, 1993.
[7] Lakshmikantham, V., Wen, L. and Zhang, B., Theory of Differential Equations with Unbounded Delay, Kluwer, Dordrecht, 1994.
[8] Muresan, V., Differential Equations with Affine Modified Argument (Romanian), Transilvania Press, Cluj, 1997.
[9] Precup, R., Analysis of some neutral delay differential equations, Studia Univ. Babe¸sBolyai Math., to appear.
[10] Precup, R. and Kirr, E., Analysis of a nonlinear integral equation modelling infectious diseases, Proc. Internat. Conf. Timi¸soara, 19-21 May 1997, 178-195.
[11] Rus, I.A., Principles and Applications of the Fixed Point Theory (Romanian), Dacia, Cluj, 1979.