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Existence principles for Carathéodory differential equations in Banach spaces. (English) Zbl 0790.34054
The authors are introducing the notion of “\(K\)-Carathéodory function” in infinite dimensional Banach spaces. \(K\)-Carathéodory is stronger than Carathéodory. In finite dimensions these two notions are equivalent. Then the authors are investigating boundary value problems for ODE with \(K\)-Carathéodory right hand side.

MSC:
34G20 Nonlinear differential equations in abstract spaces
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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