Systems of functional differential equations with maxima, of mixed type

Abstract

In this paper we study some properties of the solutions of a second order system of functional differential equations with maxima, of mixed type, with “boundary” conditions. We use Perov’s fixed point theorem and the weakly Picard operator technique.

Authors

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

Keywords

Perov’s fixed point theorem, weakly Picard operator, equations of mixed type, equations with maxima.

Cite this paper as:

D. Otrocol, Systems of functional differential equations with maxima, of mixed type, Electron. J. Qual. Theory Differ. Equ., Vol. 2014 (2014), No. 5, pp. 1–9;

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About this paper

Journal

Electronic Journal of Qualitative Theory of Differential Equations

Publisher Name

Univ. Szeged, Hungary

Print ISSN

1417-3875

Online ISSN
MR

MR3183603

ZBL

Google Scholar

[1] D. D. BAINOV, N. G. KAZAKOVA, A finite difference method for solving the periodic problem for autonomous differential equations with maxima, Math. J. Toyama Univ. 15(1992), 1–13. MR1195436

[2] D. D. BAINOV, S. HRISTOVA, Differential equations with maxima, Chapman & Hall/CRC Pure and Applied Mathematics, 2011.

[3] V. A. DÂRZU, Data dependence for functional differential equations of mixed types, Mathematica 46(2004), 61–66. MR2104023

[4] V. A. DÂRZU ILEA, Mixed functional differential equation with parameter, Studia Univ. Babes–Bolyai Math. 50(2005), 29–41. MR2245488

[5] T. JANKOWSKI, System of differential equations with maxima, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1997, No. 8, 57–60. MR1673703

[6] I. M. OLARU, An integral equation via weakly Picard operators, Fixed Point Theory 11(2010), 97–106. MR2656009

[7] I. M. OLARU, Generalization of an integral equation related to some epidemic models, Carpathian J. Math. 26(2010), 92–96. MR2676722

[8] D. OTROCOL, I. A. RUS, Functional-differential equations with “maxima” via weakly Picard operators theory, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 51(2008), 253–261. MR2433503

[9] D. OTROCOL, I. A. RUS, Functional-differential equations with maxima, of mixed type, Fixed Point Theory 9(2008), 207–220. MR2421735

[10] A. I. PEROV, A. V. KIBENKO, On a certain general method for investigation of boundary value problems, Izv. Akad. Nauk SSSR Ser. Mat. 30(1966), 249–264. MR0196534

[11] A. PETRUSEL, I. A. RUS, Fixed point theorems in L-spaces, Proc. Amer. Math. Soc. 134(2006), 411–418. MR2176009

[12] R. PRECUP, The role of the matrices that are convergent to zero in the study of semilinear operator systems, Math. Comput. Modelling 49(2009), 703–708. MR2483674

[13] I. A. RUS, Picard operators and applications, Sci. Math. Jpn. 58(2003), 191–219. MR1987831

[14] I. A. RUS, Functional differential equations of mixed type, via weakly Picard operators, Semin. Fixed Point Theory Cluj-Napoca 3(2002), 335–346. MR1929779

[15] I. A. RUS, Generalized contractions and applications, Cluj University Press, 2001. MR1947742

[16] I. A. RUS, Weakly Picard operators and applications, Semin. Fixed Point Theory Cluj-Napoca 2(2001), 41–57. MR1921517

[17] I. A. RUS, A. PETRUSEL, M. A. SERBAN, Weakly Picard operators: equivalent definitions, applications and open problems, Fixed Point Theory 7(2006), 3–22. MR2242312

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