On the existence of solutions of the differential equation with advanced argument
Abstract
In this paper the differential-functional equation
ϕ'(t) = f(t,ϕ), t∈R+
ϕ(0) = η
with an unbounded advanced argument is discovered. Under suitable assumptions, using Schauder Fixed Point Principle, a theorem on existence of solutions in a special functional-space is proved.
References
1. A. Bielecki, Równania różniczkowe zwyczajne i pewne ich uogólnienia, 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. Sci. Lublinensis 2 (1962), 70-73.
3. A. Bielecki, J. Błaż, Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument, Monatsh. 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, Monatsh. Math. 82 (1976), 1-16.
7. T. Dłotko, O istnieniu rozwiązań pewnego równania różniczkowego z wyprzedzającym argumentem, Zeszyty Naukowe WSP w Katowicach nr 4 (1964), 79-83.
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. Sci. Lublinensis 2 (1962), 70-73.
3. A. Bielecki, J. Błaż, Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichungen mit voreilendem Argument, Monatsh. 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, Monatsh. Math. 82 (1976), 1-16.
7. T. Dłotko, O istnieniu rozwiązań pewnego równania różniczkowego z wyprzedzającym argumentem, Zeszyty Naukowe WSP w Katowicach nr 4 (1964), 79-83.
MuzyczkaZ. (1985). On the existence of solutions of the differential equation with advanced argument. Annales Mathematicae Silesianae, 1, 89-92. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14338
Zofia Muzyczka
Centrum Doskonalenia Nauczycieli, Nowy Sącz Poland
Centrum Doskonalenia Nauczycieli, Nowy Sącz Poland
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