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Method of Guiding Functions in Problems of Nonlinear Analysis

  • Book
  • © 2013

Overview

Authors:
  1. Valeri Obukhovskii

    1. Department of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia

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  2. Pietro Zecca

    1. , Matematica e Informatica "U Dini", Università di Firenze, Firenze, Italy

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  3. Nguyen Van Loi

    1. Faculty of Fundamental Science, PetroVietNam University, Ba Ria, Vietnam

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  4. Sergei Kornev

    1. Department of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia

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  • May serve as the convenient introduction into intensively developing and interesting branches of contemporary nonlinear analysis, theory of differential equations and inclusions and control theory
  • The presentation is self-contained and directed to a non-specialist Contains interesting applications of the theory in control theory, theory of bifurcations and physics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2076)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Background

    • Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 1-24

  3. Method of Guiding Functions in Finite-Dimensional Spaces

    • Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 25-67

  4. Method of Guiding Functions in Hilbert Spaces

    • Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 69-104

  5. Second-Order Differential Inclusions

    • Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 105-129

  6. Nonlinear Fredholm Inclusions and Applications

    • Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 131-165

  7. Back Matter

    Pages 167-180
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Keywords

About this book

This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.

Reviews

From the reviews:

 “The central topic of this volume is the theory of guiding functions methods … . The book also collects all the related results achieved by the authors in their papers in the last 10 years. … a high-quality piece of work on the advanced theory of multimaps, and it can be quite useful and readable for graduate students and researchers in this field.” (Arsen Palestini, Mathematical Reviews, February, 2014)

“The monograph under review concerns the method of guiding functions (MGF) for solving problems of periodic oscillations in nonlinear systems. … The book is recommended for advanced graduate courses on nonlinear analysis.” (Ovidiu Cârjă, zbMATH, Vol. 1282, 2014)

Authors and Affiliations

  • Department of Physics and Mathematics, Voronezh State Pedagogical University, Voronezh, Russia

    Valeri Obukhovskii, Sergei Kornev

  • , Matematica e Informatica "U Dini", Università di Firenze, Firenze, Italy

    Pietro Zecca

  • Faculty of Fundamental Science, PetroVietNam University, Ba Ria, Vietnam

    Nguyen Van Loi

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