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 APM  Vol.2 No.5 , September 2012
Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral
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.
Cite this paper: X. Zhou and G. Ye, "Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral," Advances in Pure Mathematics, Vol. 2 No. 5, 2012, pp. 330-336. doi: 10.4236/apm.2012.25046.
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