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On the existence and uniqueness of solution of boundary-value problem for differential equations with parameter

✍ Scribed by Tadeusz Jankowski; Marian Kwapisz

Publisher: John Wiley and Sons
Year: 1976
Tongue: English
Weight: 419 KB
Volume: 71
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19760710119

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✦ Synopsis

A question of the existence of fiolutions of boundary-value problems for differential equations with parameter was considered by many authors, see [1]-[3] and [5]-[9]. The analogous problems for differential equations with a deviated argument was discussed in [8] and [3].

The purpose of this paper is t o discuss the general form of this problem by the consideration of a functional equation with parameter under a general boundary condition. I n this way we obtain a generalization of some results of [8] and [33.

Let B and B, be given BANACH spaces. By X we denote the set of the bounded functions x: I + B, I = [ 0 , a], (and Xi denotes tho subset of X containing the BOcHh-ER-integrable functions). The element r E x we write also as z(.). The

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