Temat: multivalued problem

Skocz do pozycji: 1.

Tytuł:: On the topological dimension of the solutions sets for some classes of operator and differential inclusions
Autorzy:: Bader, Ralf
Gel'man, Boris
Kamenskii, Mikhail
Obukhovskii, Valeri
Tematy:: solutions set
fixed points set
topological dimension
multivalued map
condensing map
topological degree
differential inclusion
periodic problem; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/729534.pdf Link otwiera się w nowym oknie
Opis:: In the present paper, we give the lower estimation for the topological dimension of the fixed points set of a condensing continuous multimap in a Banach space. The abstract result is applied to the fixed point set of the multioperator of the form $ = S _F$ where $_F$ is the superposition multioperator generated by the Carathéodory type multifunction F and S is the shift of a linear injective operator. We present sufficient conditions under which this set has the infinite topological dimension. In the last section of the paper, we consider the applications of the solutions sets for Cauchy and periodic problems for semilinear differential inclusions in a Banach space.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Multivalued linear operators and differential inclusions in Banach spaces
Autorzy:: Baskakov, Anatolii
Obukhovskii, Valeri
Zecca, Pietro
Tematy:: multivalued linear operator
generalized semigroup
minimal growth at infinity
Hille-Yosida condition
degenerate differential inclusion
Cauchy problem
bounded solution; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/729521.pdf Link otwiera się w nowym oknie
Opis:: In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued nonlinearities. As a consequence, we give theorems on the existence of local, global and bounded solutions of the Cauchy problem for degenerate differential inclusions.
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: An abstract Cauchy problem for higher order functional differential inclusions with infinite delay
Autorzy:: Ke, Tran
Obukhovskii, Valeri
Wong, Ngai-Ching
Yao, Jen-Chih
Tematy:: Cauchy problem
functional differential inclusion
infinite delay
higher order
existence family
phase space
fixed point
multivalued map
measure of noncompactness
condensing map; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/729357.pdf Link otwiera się w nowym oknie
Opis:: The existence results for an abstract Cauchy problem involving a higher order differential inclusion with infinite delay in a Banach space are obtained. We use the concept of the existence family to express the mild solutions and impose the suitable conditions on the nonlinearity via the measure of noncompactness in order to apply the theory of condensing multimaps for the demonstration of our results. An application to some classes of partial differential equations is given.
Dostawca treści:: Biblioteka Nauki

Artykuł

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