Classical solutions of functional partial differential inequalities with initial boundary conditions are estimated by maximal solutions of suitable problems for ordinary functional differential equations. Uniqueness of solutions and continuous dependence on given functions are obtained as applications of the comparison result. A theorem on weak functional differential inequalities generated by mixed problems is proved. Our method is based on an axiomatic approach to equations with unbounded delay. Examples of phase spaces are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-2,
author = {Z. Kamont and S. Kozie\l },
title = {Functional differential inequalities with unbounded delay},
journal = {Annales Polonici Mathematici},
volume = {89},
year = {2006},
pages = {19-37},
zbl = {1111.35139},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-2}
}
Z. Kamont; S. Kozieł. Functional differential inequalities with unbounded delay. Annales Polonici Mathematici, Tome 89 (2006) pp. 19-37. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap88-1-2/