We consider the existence of extremal solutions to second order discontinuous implicit ordinary differential equations with discontinuous implicit boundary conditions in ordered Banach spaces. We also study the dependence of these solutions on the data, and cases when the extremal solutions are obtained as limits of successive approximations. Examples are given to demonstrate the applicability of the method developed in this paper.
@article{bwmeta1.element.bwnjournal-article-apmv71z1p1bwm,
author = {S. Carl and S. Heikkil\"a},
title = {On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions},
journal = {Annales Polonici Mathematici},
volume = {72},
year = {1999},
pages = {1-17},
zbl = {0981.34051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv71z1p1bwm}
}
S. Carl; S. Heikkilä. On discontinuous implicit differential equations in ordered Banach spaces with discontinuous implicit boundary conditions. Annales Polonici Mathematici, Tome 72 (1999) pp. 1-17. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv71z1p1bwm/
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