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

  • Victor Zvyagin
  • Valeri Obukhovskii
  • Andrey Zvyagin


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.


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 

Mathematics Subject Classification

Primary 49K21 Secondary 34A60 34G25 34H05 47H04 47H11 49J15 49J21 49K15 55M20 58B15 76A05 93C10 93C15 93C25 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Victor Zvyagin
    • 1
  • Valeri Obukhovskii
    • 2
  • Andrey Zvyagin
    • 3
  1. 1.Faculty of MathematicsVoronezh State UniversityVoronezhRussia
  2. 2.Faculty of Physics and MathematicsVoronezh State Pedagogical UniversityVoronezhRussia
  3. 3.Research Institute of MathematicsVoronezh State UniversityVoronezhRussia

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