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In this paper, we use a new fixed point theorem to study semilinear evolution equations with the initial conditions in Banach spaces. The results obtained here improve and generalize many known results.
In this paper we apply the technique of measures of noncompactness to the theory of infinite system of differential equations in the Banach sequence spaces ℓp(1≤p<∞). Our aim is to present some existence results for infinite system of differential equations formulated with the help of measures of noncompactness.
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