Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1997-09-30
About the Existence of Solutions of a Boundary Value Problem for a Carathéodory Differential SystemG. Anichini and Giuseppe Conti (1) Università di Modena e Reggio Emilia, Italy
(2) Università degli Studi di Firenze, Italy
A boundary value problem of the form $x’ = f(t,x), x \in S$ is considered where $f$ is a Carathéodory function and $S$ is a suitable boundary constraint. A related integral equation with an exact number of solutions is studied, in order to show the existence of solutions of the boundary value problem through a fixed point theorem for $w$-maps in the Darbo sense.
Keywords: Solutions set, isolated points, number of solutions, integral equations, boundary value problems
Anichini G., Conti Giuseppe: About the Existence of Solutions of a Boundary Value Problem for a Carathéodory Differential System. Z. Anal. Anwend. 16 (1997), 621-630. doi: 10.4171/ZAA/781