On the density of extremal solutions of differential inclusions
Volume 56 / 1992
Annales Polonici Mathematici 56 (1992), 133-142
DOI: 10.4064/ap-56-2-133-142
Abstract
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].
