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© 2013

Method of Guiding Functions in Problems of Nonlinear Analysis

Benefits

  • 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

Book

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 1-24
  3. Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 25-67
  4. Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 69-104
  5. Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 105-129
  6. Valeri Obukhovskii, Pietro Zecca, Nguyen Van Loi, Sergei Kornev
    Pages 131-165
  7. Back Matter
    Pages 167-180

About this book

Introduction

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.

Keywords

34C25, 34C23, 47J15, 58E07, 34C15, 34B15, 34A60, 34G25 Guiding function bifurcation control system periodic solution

Authors and affiliations

  1. 1.Department of Physics and MathematicsVoronezh State Pedagogical UniversityVoronezhRussia
  2. 2., Matematica e Informatica "U Dini"Università di FirenzeFirenzeItaly
  3. 3.Faculty of Fundamental SciencePetroVietNam UniversityBa RiaVietnam
  4. 4.Department of Physics and MathematicsVoronezh State Pedagogical UniversityVoronezhRussia

Bibliographic information

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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)