Temat: compact perturbations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Sets in the ranges of nonlinear accretive operators in Banach spaces
Autorzy:: Kartsatos, Athanassios G.
Powiązania:: https://bibliotekanauki.pl/articles/1289125.pdf
Data publikacji:: 1995
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: accretive operator
m-accretive operator
compact perturbations
compact resolvents
Leray-Schauder boundary condition
mapping theorems
Opis:: Let X be a real Banach space and G ⊂ X open and bounded. Assume that one of the following conditions is satisfied: (i) X* is uniformly convex and T:Ḡ→ X is demicontinuous and accretive; (ii) T:Ḡ→ X is continuous and accretive; (iii) T:X ⊃ D(T)→ X is m-accretive and Ḡ ⊂ D(T). Assume, further, that M ⊂ X is pathwise connected and such that M ∩ TG ≠ ∅ and $M ∩ \overline{T(∂ G)} = ∅$. Then $M ⊂ \overline{TG}$. If, moreover, Case (i) or (ii) holds and T is of type $(S_1)$, or Case (iii) holds and T is of type $(S_2)$, then M ⊂ TG. Various results of Morales, Reich and Torrejón, and the author are improved and/or extended.
Źródło:: Studia Mathematica; 1995, 114, 3; 261-273
0039-3223
Pojawia się w:: Studia Mathematica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
Autorzy:: Gudovich, Anastasie
Kamenski, Mikhail
Nistri, Paolo
Powiązania:: https://bibliotekanauki.pl/articles/729318.pdf
Data publikacji:: 2001
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: singular perturbations
differential inclusions
analytic semigroups
multivalued compact operators
Lipschitz selections
Opis:: We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

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