De Pascale, Espedito; Lewicki, Grzegorz; Marino, Giuseppe Some conditions for compactness in \(BC(Q)\) and their application to boundary value problems. (English) Zbl 1018.46014 Analysis, München 22, No. 1, 21-32 (2002). 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. Cited in 1 ReviewCited in 3 Documents 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 Keywords:oscillations; compactness; boundary value problems on unbounded intervals PDFBibTeX XMLCite \textit{E. De Pascale} et al., Analysis, München 22, No. 1, 21--32 (2002; Zbl 1018.46014) Full Text: DOI