Properties of the solutions of a system of differential equations with maxima, via weakly picard operator theory

Abstract

In this paper we present some properties of the solutions of a system of differential equation with maxima. Existence, uniqueness, inequalities of ˇCaplygin type and data  dependence (monotony, continuity) results for the solution of the Cauchy problem of this system are obtained using weakly Picard operator technique.

Authors

D. Otrocol
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,

Keywords

Differential equations with maxima, data dependence, Picard operator technique

Cite this paper as:

D. Otrocol, Properties of the solutions of a system of differential equations with maxima, via weakly picard operator theory, Commun. Appl. Anal. Vol. 17 (2013), no. 1, pp. 99–108

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DOI
Print ISSN

1083-2564

Online ISSN
MR

MR3075771

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References

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[3] P. Gonzales, M. Pinto, Component-wise conditions for the asymptotic equivalence for nonlinear differential equations with maxima, Dynamic Systems and Applications, 20 (2011), 439–454.

[4] D. Otrocol, I.A. Rus, Functional-differential equations with “maxima” via weakly Picard operators theory, Bull. Math. Soc. Sci. Math. Roumanie, 51(99) (2008), No. 3, 253–261.

[5] D. Otrocol, I.A. Rus, Functional-differential equations with maxima of mixed type argument, Fixed Point Theory, 9 (2008), no. 1, pp. 207–220.

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[7] I.A. Rus, Generalized contractions, Cluj University Press, 2001.

[8] I.A. Rus, Functional-differential equations of mixed type, via weakly Picard operators, Seminar on fixed point theory, Cluj-Napoca, 3(2002), 335-345.

[9] E. Stepanov, On solvability of same boundary value problems for differential equations with “maxima”, Topological Methods in Nonlinear Analysis, 8 (1996), 315–326.

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