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Y. P. Lu, G. J. Ye and Y. Wang, “The Darboux Problem Involving the Distributional Henstock-Kurzweil Integral,” Proceedings of the Edinburgh Mathematical Society, Vol. 55, No. 1, 2012, pp. 197-205.

has been cited by the following article:

• TITLE: Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral

  AUTHORS: Xueyuan Zhou, Guoju Ye

  KEYWORDS: Periodic Boundary Value Problem; Distributional Henstock-Kurzweil Integral; Distributional Derivative; Existence; Upper and Lower Solutions; Fixed Point

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.5, September 26, 2012

  ABSTRACT: We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.