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

DOI: 10.4236/apm.2012.25046, PP. 330-336

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

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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.


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