An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].
@article{bwmeta1.element.bwnjournal-article-apmv56z2p133bwm,
author = {F. S. De Blasi and G. Pianigiani},
title = {On the density of extremal solutions of differential inclusions},
journal = {Annales Polonici Mathematici},
volume = {57},
year = {1992},
pages = {133-142},
zbl = {0760.34019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv56z2p133bwm}
}
F. S. De Blasi; G. Pianigiani. On the density of extremal solutions of differential inclusions. Annales Polonici Mathematici, Tome 57 (1992) pp. 133-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv56z2p133bwm/
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