We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a partial explanation as to why the contraction mapping principle is not a viable tool for boundary value problems at resonance.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-5,
author = {Alaa Almansour and Paul Eloe},
title = {Fixed points and solutions of boundary value problems at resonance},
journal = {Annales Polonici Mathematici},
volume = {113},
year = {2015},
pages = {263-274},
zbl = {06493362},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-5}
}
Alaa Almansour; Paul Eloe. Fixed points and solutions of boundary value problems at resonance. Annales Polonici Mathematici, Tome 113 (2015) pp. 263-274. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap115-3-5/