On first-order periodic boundary value problems and distributional Henstock-Kurzweil integrals

Abstract

This paper is devoted to the study of existence and dependence of solutions of the first-order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The methods used are mainly the method of upper and lower solutions and a fixed point theorem.

The Distributional Henstock-Kurzweil Integral and Applications: A Survey

“…Remark 5.3. The Schauder's fixed point theorem and the Vidossich theorem can also be applied to study the existence of solutions and the structure of the set of solutions of the wave equation [27], the periodic boundary value problem [24], the nonlinear multi-point boundary value problem [23].…”

“…Let T be a continuous map of M into a compact subset K of M. Then T has a fixed point. Now, we show the applications of the D HK integral in integral and differential equations[20,[22][23][24][25][26][27].…”

On first-order periodic boundary value problems and distributional Henstock-Kurzweil integrals

“…In Section  we define the distributional Henstock-Kurzweil integral or briefly the D HK -integral. We say that a distribution f is D HK -integrable ©2014 Liu et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.…”