On inclusions with multivalued operators and their applications to some optimization problems

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• 作者：Victor Zvyagin ; Valeri Obukhovskii…
• 关键词：Primary 49K21 ; Secondary 34A60 ; 34G25 ; 34H05 ; 47H04 ; 47H11 ; 49J15 ; 49J21 ; 49K15 ; 55M20 ; 58B15 ; 76A05 ; 93C10 ; 93C15 ; 93C25 ; Optimization ; optimal control ; feedback control ; operator inclusion ; differential inclusion ; Filippov implicit function lemma ; multivalued map ; Fredholm map ; fixed point ; topological degree ; coincidence degree ; non ; Newtonian fluid
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：16
• 期：1-2
• 页码：27-82
• 全文大小：1,784 KB
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• 作者单位：Victor Zvyagin (1)
  Valeri Obukhovskii (2)
  Andrey Zvyagin (3)
  
  1. Faculty of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394006, Voronezh, Russia
  2. Faculty of Physics and Mathematics, Voronezh State Pedagogical University, 394043, Voronezh, Russia
  3. Research Institute of Mathematics, Voronezh State University, Universitetskaya pl., 1, 394006, Voronezh, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

In the present survey paper, we discuss applications of differential and operator inclusions to some optimization and optimal control problems. The Filippov implicit function lemma is considered and its application to the optimization of a feedback control system governed by a semilinear differential equation in a Banach space is presented. We describe the construction of the oriented coincidence degree for a compact multivalued perturbation of a nonlinear Fredholm operator and apply it to an optimal control problem induced by an ordinary differential equation with the Hopf boundary condition. We study also an optimal feedback control problem for a mathematical model of the motion of weakly concentrated water polymer solutions.