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

Xueyuan Zhou, Guoju Ye

Department of Mathematics, Hohai University, Nanjing, P. R. China.

DOI: 10.4236/apm.2012.25046                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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