On functional-differential equations with advancing argument

Zofia Muzyczka

Published: 1986-09-30

Vol. 2 (1986)

On functional-differential equations with advancing argument

Zofia Muzyczka

Abstract

The literature devoted to differential-functional equations with advancing argument is rather scarce. In the papers [1], [2], [4], [7] the existence of solutions of Cauchy problem and in [5], [6] and [8] - of Nicoletti problem for differential-functional equations with bounded advancement of argument are investigated. The differential-functional equations with unbounded advancement of argument are considered in the articles [3] and [9]. Namely in [3] the existence and uniqueness of solution of the Nicoletti problem is proved, and in [9] an existence theorem for the Cauchy problem is given. The purpose of this paper is to formulate an existence theorem for the Nicoletti problem in the case where the advancement of the argument is unbounded. The proof of this theorem is based on Schauder’s fixed point theorem.

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Muzyczka, Z. (1986). On functional-differential equations with advancing argument. Annales Mathematicae Silesianae, 2, 60–64. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14322

References

1. A. Bielecki, Ordinary differential equations and some their generalisations (in Polish), Warszawa 1961.
2. A. Bielecki, Certaines conditions suffisantes pour l'existence d'une solution de l'equation ϕ'(t)=F(t,ϕ(t),ϕ(v(t))), Folia Soc. Sc. Lublinensis 2 (1962), 70-73.
3. A. Bielecki, J. Błaż, Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichung mit voreilendem Argument, Monatsch. Math. 88 (1979), 287-291.
4. J. Błaż, Sur l'existence d'une solution d'une équation différentielle à argument avancé, Ann. Polon. Math. 15 (1964), 1-8.
5. J. Błaż, Über die Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument, Arch. Math. 27 (1976), 529-534.
6. J. Błaż, W. Walter, Über Funktional-Differentialgleichungen mit voreilendem Argument, Monatsch. Math. 82 (1976), 1-16.
7. T. Dłotko, On the existence of solutions of some differential equation with advancing argument, (in Polish), Zeszyty Nauk. Wyż. Szkoły Ped. w Katowicach 4 (1964), 79-83.
8. T. Dłotko, The application of the vector-field’s rotation in the theory of differential equations and their generalizations (in Polish), Uniw. Śląski w Katowicach (1971).
9. Z. Muzyczka, On the existence of solutions of the differential equation with advanced argument, Ann. Math. Sil. 1 (13) (1985), 89-92. Google Scholar

Vol. 2 (1986)
Published: 1986-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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