In this paper, an existence theorem for nth order perturbed differential inclusion is proved under the mixed Lipschitz and Carathéodory conditions. The existence of extremal solutions is also obtained under certain monotonicity conditions on the multi-functions involved in the inclusion. Our results extend the existence results of Dhage et al. [7,8] and Agarwal et al. [1].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1064,
author = {Bupurao C. Dhage and Adrian Petru\c sel},
title = {The method of upper and lower solutions for perturbed nth order differential inclusions},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {26},
year = {2006},
pages = {57-76},
zbl = {1139.34005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1064}
}
Bupurao C. Dhage; Adrian Petruşel. The method of upper and lower solutions for perturbed nth order differential inclusions. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 26 (2006) pp. 57-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1064/
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