Monotone iteration method for differential equations involving integral boundary conditions on the half line

Abstract

By applying the monotone iterative methods, we obtain the existence of monotone positive solutions for integral boundary value problems of differential equations on the half line, and establish the iterative schemes for approximating the solutions. Our approach is based on the fixed point theorem and the monotone iterative technique. The existence of lower and upper solutions is not needed.

Keywords:

• second-order differential equation on the half line
• boundary value problem
• monotone iterative method
• iterative scheme

AMS Subject Classifications::

• 34B10
• 34B15
• 35B10
• 65Q05

Acknowledgements

The author would like to thank the anonymous referees for their careful reading of this manuscript and for suggesting some useful rhetorical changes. This research is supported by Natural Science Foundation of Guangdong province (No: 7004569) and the Foundation for High-level talents in Guangdong Higher Education Project.