Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznan, Poland, e-mail: mcichon@amu.edu.pl
Abstract: In this paper we prove an existence theorem for the Cauchy problem
x'(t) = f(t, x(t)), \quad x(0) = x_0, \quad t \in I_{\alpha} = [0, \alpha]
using 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.
Keywords: pseudo-solution, Pettis integral, Henstock-Kurzweil integral, Cauchy problem
Classification (MSC 2000): 34G20, 28B05
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