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1991-1992 | 56 | 2 | 133-142
Tytuł artykułu

On the density of extremal solutions of differential inclusions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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].
Słowa kluczowe
Rocznik
Tom
56
Numer
2
Strony
133-142
Opis fizyczny
Daty
wydano
1992
otrzymano
1990-01-03
poprawiono
1990-08-01
Twórcy
  • Dipartimento di Matematica, Università di Roma II, via Fontanile di Carcaricola, 00133 Roma, Italy
  • Istituto di Matematica, Università di Siena, via del Capitano 15, 53100 Siena, Italy
Bibliografia
  • [1] A. Antosiewicz and A. Cellina, Continuous selections and differential relations, J. Differential Equations 19 (1975), 386-398.
  • [2] J. P. Aubin and A. Cellina, Differential Inclusions, Springer, Berlin 1984.
  • [3] S. Bahi, Quelques propriétés topologiques de l'ensemble des solutions d'une classe d'équations différentielles multivoques (II), Séminaire d'Analyse Convexe, Montpellier, 1983, exposé No. 4.
  • [4] A. Bressan and G. Colombo, Generalized Baire category and differential inclusions in Banach spaces, J. Differential Equations 76 (1988), 135-158.
  • [5] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin 1977.
  • [6] G. Choquet, Lectures on Analysis, Benjamin, Reading 1969.
  • [7] P. V. Chuong, Un résultat d'existence de solutions pour des équations différentielles multivoques, C. R. Acad. Sci. Paris 301 (1985), 399-402.
  • [8] F. S. De Blasi and G. Pianigiani, A Baire category approach to the existence of solutions of multivalued differential equations in Banach spaces, Funkcial. Ekvac. (2) 25 (1982), 153-162.
  • [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.
  • [10] F. S. De Blasi and G. Pianigiani, Differential inclusions in Banach spaces, J. Differential Equations 66 (1987), 208-229.
  • [11] A. F. Filippov, The existence of solutions of generalized differential equations, Math. Notes 10 (1971), 608-611.
  • [12] A. N. Godunov, Peano's theorem in Banach spaces, Funktsional. Anal. i Prilozhen. 9 (1) (1974), 59-60 (in Russian).
  • [13] H. Kaczyński and C. Olech, Existence of solutions of orientor fields with nonconvex right hand side, Ann. Polon. Math. 29 (1974), 61-66.
  • [14] N. S. Papageorgiou, On the solution set of differential inclusions in Banach spaces, Appl. Anal. 25 (1987), 319-329.
  • [15] N. S. Papageorgiou, On measurable multifunctions with applications to random multivalued equations, Math. Japon. 32 (1987), 437-464.
  • [16] G. Pianigiani, On the fundamental theory of multivalued differential equations, J. Differential Equations 25 (1977), 30-38.
  • [17] A. A. Tolstonogov, On differential inclusions in Banach spaces, Soviet Math. Dokl. 20 (1979), 186-190.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv56z2p133bwm
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