In this paper we determine the Hausdorff measure of noncompactness on the sequence space $n(\phi)$ of W. L. C. Sargent. Further we apply the technique of measures of noncompactness to the theory of infinite systems of differential equations in the Banach sequence spaces $n(\phi)$ and $m(\phi)$. Our aim is to present some existence results for infinite systems of differential equations formulated with the help of measures of noncompactness.

Keywords:

sequence spaces, BK spaces, measure of noncompactness, infinite system of differential equations sequence spaces, BK spaces, measure of noncompactness, infinite system of differential equations

MSC Classifications:

46B15, 46B45, 46B50, 34A34, 34G20 show english descriptions Summability and bases [See also 46A35]
Banach sequence spaces [See also 46A45]
Compactness in Banach (or normed) spaces
Nonlinear equations and systems, general
Nonlinear equations [See also 47Hxx, 47Jxx] 46B15 - Summability and bases [See also 46A35]
46B45 - Banach sequence spaces [See also 46A45]
46B50 - Compactness in Banach (or normed) spaces
34A34 - Nonlinear equations and systems, general
34G20 - Nonlinear equations [See also 47Hxx, 47Jxx]

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