On the density of extremal solutions of differential inclusions

F. S. De Blasi; G. Pianigiani

Annales Polonici Mathematici (1992)

  • Volume: 56, Issue: 2, page 133-142
  • ISSN: 0066-2216

Abstract

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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].

How to cite

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F. S. De Blasi, and G. Pianigiani. "On the density of extremal solutions of differential inclusions." Annales Polonici Mathematici 56.2 (1992): 133-142. <http://eudml.org/doc/262527>.

@article{F1992,
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].},
author = {F. S. De Blasi, G. Pianigiani},
journal = {Annales Polonici Mathematici},
keywords = {differential inclusions; extremal solutions; Choquet function; Banach space; Baire-category theorem},
language = {eng},
number = {2},
pages = {133-142},
title = {On the density of extremal solutions of differential inclusions},
url = {http://eudml.org/doc/262527},
volume = {56},
year = {1992},
}

TY - JOUR
AU - F. S. De Blasi
AU - G. Pianigiani
TI - On the density of extremal solutions of differential inclusions
JO - Annales Polonici Mathematici
PY - 1992
VL - 56
IS - 2
SP - 133
EP - 142
AB - 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].
LA - eng
KW - differential inclusions; extremal solutions; Choquet function; Banach space; Baire-category theorem
UR - http://eudml.org/doc/262527
ER -

References

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  9. [9] F. S. De Blasi and G. Pianigiani, The Baire category method in existence problems for a class of multivalued differential equations with nonconvex right hand side, Funkcial. Ekvac. 28 (1985), 139-156. Zbl0584.34007
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