Canad. Math. Bull. 56(2013), 388-394
Printed: Jun 2013
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.
sequence spaces, BK spaces, measure of noncompactness, infinite system of differential equations
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]