Continuous selector of representative measures and the space of faces of a convex compactum

1977 ◽  
Vol 22 (6) ◽  
pp. 991-996
Author(s):  
N. N. Makarov
Keyword(s):  
Convex Compactum ◽  
Continuous Selector

scholarly journals On the structure of the solution set of evolution inclusions with Fréchet subdifferentials

2000 ◽  
Vol 13 (1) ◽  
pp. 51-72 ◽  
Author(s):  
Tiziana Cardinali
Keyword(s):  
Cauchy Problem ◽  
Type Theorem ◽  
Periodic Problem ◽  
Solution Set ◽  
Evolution Inclusions ◽  
Continuity Result ◽  
Continuous Selector ◽  
The Cauchy Problem ◽  
Fréchet Subdifferentials ◽  
Real Separable Hilbert Space

In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o ∂−f of a function f:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone . subdifferential of order two and a perturbation F:I×Ω→Pfc(H) with nonempty, closed and convex values.First we show that the Cauchy problem has a nonempty solution set which is an Rδ-set in C(I,H), in particular, compact and acyclic. Moreover, we obtain a Kneser-type theorem. In addition, we establish a continuity result about the solution-multifunction x→S(x). We also produce a continuous selector for the multifunction x→S(x). As an application of this result, we obtain the existence of solutions for a periodic problem.

Isolated faces of a convex compactum

1979 ◽  
Vol 25 (1) ◽  
pp. 73-77
Author(s):  
V. P. Fedotov
Keyword(s):  
Convex Compactum
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