×

Some conditions for compactness in \(BC(Q)\) and their application to boundary value problems. (English) Zbl 1018.46014

Summary: In this note we present some simple corollaries of an old result of Bartle, characterizing the compactness in the space \(BC(Q)\) of continuous and bounded real functions defined on a topological space \(Q\). We formulate remarks to obtain conditions for a subset \(F\) of \(BC(Q)\) to be relatively compact. Some examples and counterexamples shedding light on the structure of compact subsets in \(BC(Q)\) are constructed. The results seem to be very useful in the study of boundary value problems on unbounded intervals.

MSC:

46B50 Compactness in Banach (or normed) spaces
34B15 Nonlinear boundary value problems for ordinary differential equations
40E15 Lacunary inversion theorems
54C35 Function spaces in general topology
PDFBibTeX XMLCite
Full Text: DOI