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

DOI: 10.4236/apm.2012.25046   PDF   HTML   XML   3,650 Downloads   6,148 Views   Citations

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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