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.