The unique symmetric positive solutions for nonlinear fourth order arbitrary two-point boundary value problems: a fixed point theory approach
Abstract
In this paper, we explore the existence and uniqueness of positive solutions for the following nonlinear fourth order ordinary differential equation u^(4)(t)=f(t,u(t)). Here we also demonstrate that under certain assumptions the above boundary value problem exist a unique symmetric positive solution. The analysis of this paper is based on a fixed point theorem in partially ordered metric spaces due to Amini-Harandi and Emami. The results of this paper generalize the results of several authors in literature. Finally, we provide some illustrative examples to support our analytic proof.
Copyright © 2019 Md. Asaduzzaman, Md. Zulfikar Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
M. Asaduzzaman, M. Zulfikar Ali, The unique symmetric positive solutions for nonlinear fourth order arbitrary two-point boundary value problems: a fixed point theory approach, Adv. Fixed Point Theory 9 (2019), 80–98. https://doi.org/10.28919/afpt/3959
BibTeX
@article{Asaduzzaman2019,
author = {Asaduzzaman, Md. and Zulfikar Ali, Md.},
title = {The unique symmetric positive solutions for nonlinear fourth order arbitrary two-point boundary value problems: a fixed point theory approach},
journal = {Adv. Fixed Point Theory},
volume = {9},
year = {2019},
pages = {80--98},
doi = {10.28919/afpt/3959}
}