On functional-differential equations with advancing argument
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.
References
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3. A. Bielecki, J. Błaż, Über eine Verallgemeinerung der Nicoletti-Aufgabe für Funktional-Differentialgleichung mit voreilendem Argument, Monatsch. Math. 88 (1979), 287-291.
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Centrum Doskonalenia Nauczycieli, Nowy Sącz Poland
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