Hybrid differential equations with maxima via Picard operators theory

Abstract

The aim of this paper is to discuss some basic problems (existence and uniqueness, data dependence) of the Cauchy problem for a hybrid differential equation with maxima using weakly Picard operators technique.

Authors

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

Keywords

Differential equations with maxima, Cauchy problem, data dependence, weakly Picard operators.

Cite this paper as:

D. Otrocol, Hybrid differential equations with maxima via Picard operators theory, Stud. Univ. Babes-Bolyai Math., 61 (2016) no. 4, pp. 421-428.

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About this paper

Journal

Studia Universitatis Babes-Bolyai Mathematica

Publisher Name

Univ. Babes-Bolyai, Cluj-Napoca, Romania

DOI
Print ISSN

0252-1938

Online ISSN

2065-961X

MR

MR3583207

ZBL

1397.34108

Google Scholar

[1] Bainov, D.D., Hristova, S., Differential equations with maxima, Chapman & Hall/CRC Pure and Applied Mathematics, 2011.

[2] Bainov, D.D., Petrov, V.A., Proyteheva, V.S., Existence and asymptotic behavior of nonoscillatory solutions of second order neutral differential equations with “maxima”, J. Comput. Appl. Math., 83(1997), no. 2, 237-249.

[3] Dhage, B.C., Lakshmikantham, V., Basic results on hybrid differential equations, Nonlinear Anal. Hybrid Syst., 4(2010), 414-424.

[4] Dobritoiu, M., Rus, I.A., Serban, M.A., An integral equation arising from infections diseases, via Picard operators, Stud. Univ. Babe¸s-Bolyai Math., 52(2007), no. 3, 81-94.

[5] Georgiev, L., Angelov, V.G., On the existence and uniqueness of solutions for maximum equations, Glas. Mat., 37(2002), no. 2, 275-281.

[6] Hale, J., Theory of functional differential equations, Springer, 1977.

[7] Otrocol, D., Systems of functional differential equations with maxima, of mixed type, Electron. J. Qual. Theory Differ. Eq., 2014(2014), no. 5, 1-9.

[8] Otrocol, D., Ilea, V.A., Qualitative properties of a functional differential equation, Electron. J. Qual. Theory Differ. Eq., 47(2014), 1-8.

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

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

[11] Precup, R., Monotone techniques to the initial values problem for a delay integral equation from Biomathematics, Stud. Univ. Babes-Bolyai Math., 40(1995), no. 2, 63-73.

[12] Rus, I.A., Picard operators and applications, Sci. Math. Jpn., 58(2003), no. 1, 191-219.

[13] Rus, I.A., Functional differential equations of mixed type, via weakly Picard operators, Seminar on Fixed Point Theory Cluj-Napoca, 3(2002), 335-346.

[14] Rus, I.A., Generalized contractions and applications, Cluj University Press, 2001.

[15] Rus, I.A., Weakly Picard operators and applications, Seminar on Fixed Point Theory, Cluj-Napoca, 2(2001), 41-58.

[16] Stepanov, E., On solvability of same boundary value problems for differential equations with “maxima“, Topol. Methods Nonlinear Anal., 8(1996), 315-326.

[17] Zhang, B.G., Zhang, G., Qualitative properties of functional equations with “maxima”, Rocky Mountain J. Math., 29(1999), no. 1, 357-367.

2016

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