Cianciaruso, Filomena; Colao, Vittorio; Marino, Giuseppe; Xu, Hong-Kun A compactness result for differentiable functions with an application to boundary value problems. (English) Zbl 1275.46020 Ann. Mat. Pura Appl. (4) 192, No. 3, 407-421 (2013). 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. Cited in 2 Documents 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 Keywords:compactness; Ascoli-Arzela theorem; differentiable function; boundary value problem PDFBibTeX XMLCite \textit{F. Cianciaruso} et al., Ann. Mat. Pura Appl. (4) 192, No. 3, 407--421 (2013; Zbl 1275.46020) Full Text: DOI References: [1] Avramescu, C., Sur l’existence des solutions convergentes des systémes d’équations différentielles non linéaires, Ann. Mat. Pura Appl., 4, 147-168 (1969) · Zbl 0196.10701 [2] Banas, J., Goebel, K.: Measures of noncompactness in banach spaces. In: Lecture Notes in Pure and Applied Mathematics, vol. 60. Dekker, New York (1980) · Zbl 0441.47056 [3] Bartle, R. G., On compactness in functional analysis, Trans. Am. Math. Soc., 79, 35-57 (1955) · Zbl 0064.35503 [4] Deimling, K., Multivalued Differential Equations (1992), Berlin: Walter de Gruyter, Berlin · Zbl 0760.34002 [5] De Pascale, E.; Lewicki, G.; Marino, G., Some conditions for compactness in \({\mathcal{BC}(Q)}\) and their application to boundary value problems, Analysis, 22, 21-32 (2002) · Zbl 1018.46014 [6] Liu, Z., Liu, L., Wu, Y., Zhao, J.: Unbounded solutions of a boundary value problem for abstract nth-order differential equations on a infinite interval. J. Appl. Math. Stoch. Anal. 11. Art. ID 589480 (2008) [7] Xiao, Y. B.; Kim, J. K.; Huang, N. J., A generalization of Ascoli-Arzela theorem with an application, Nonlinear Funct. Anal. Appl., 11, 2, 305-317 (2006) · Zbl 1113.46013 [8] Zeidler, E., Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems (1985), Berlin: Springer, Berlin This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.