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darboux problem

Proceedings of the Edinburgh Mathematical Society (1)

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The Darboux problem involving the distributional Henstock–Kurzweil integral
Part of
Yueping Lu, Guoju Ye, Ying Wang, Wei Liu
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 55 / Issue 1 / February 2012

Published online by Cambridge University Press:

04 January 2012, pp. 197-205
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In this paper, using the Schauder Fixed Point Theorem and the Vidossich Theorem, we study the existence of solutions and the structure of the set of solutions of the Darboux problem involving the distributional Henstock–Kurzweil integral. The two theorems presented in this paper are extensions of the previous results of Deblasi and Myjak and of Bugajewski and Szufla.