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Existence results for differential equations in Banach spaces. (English) Zbl 0786.34069
This article is devoted to some generalizations of classical existence results for finite systems of ordinary differential equations onto ordinary differential equations in Banach spaces. The Cauchy problem and two-point boundary-value problem are considered; in this connection the condition of compactness of the corresponding integral operator is supposed and namely this fact allows to use usual ‘finite-dimensional’ ideas and methods in this field; one can notice that this condition is difficult to understand and usually is true only when the right hand side of the equation considered is a completely continuous function.
Reviewer: P.Zabrejko (Minsk)

MSC:
34G20 Nonlinear differential equations in abstract spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34G10 Linear differential equations in abstract spaces
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