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A compactness result for differentiable functions with an application to boundary value problems. (English) Zbl 1275.46020

Summary: We characterize the relative compactness of subsets of the space \({\mathcal{BC}^m([0,+\infty [;E)}\) of bounded and \(m\)-differentiable functions defined on \([0,+\infty [\) with values in a Banach space \(E\). Moreover, we apply this characterization to prove the existence of solutions of a boundary value problem in Banach spaces.

MSC:

46E40 Spaces of vector- and operator-valued functions
46E15 Banach spaces of continuous, differentiable or analytic functions
46B50 Compactness in Banach (or normed) spaces
34B40 Boundary value problems on infinite intervals for ordinary differential equations
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