THE HENSTOCK-KURZWEIL-PETTIS INTEGRALS AND EXISTENCE THEOREMS FOR THE CAUCHY PROBLEM


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Abstract

In this paper we prove an existence theorem for the Cauchy problemusing the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function f are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function f satisfies some conditions expressed in terms of measures of weak noncompactness.

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