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# Application of Measure of Noncompactness to Infinite Systems of Differential Equations

Published:2011-08-31
Printed: Jun 2013
• M. Mursaleen,
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
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## Abstract

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
 MSC Classifications: 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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