Application of Measure of Noncompactness to Infinite Systems of Differential Equations

Mursaleen, M.

Canadian mathematical bulletin, Tome 56 (2013) no. 2, pp. 388-394

Résumé

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

Détail

DOI : 10.4153/CMB-2011-170-7

Mots-clés : 46B15, 46B45, 46B50, 34A34, 34G20, sequence spaces, BK spaces, measure of noncompactness, infinite system of differential equations

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