Kirchhoff Equations
A Variational Approach
1st Edition
Will be published approx. on 26. August 2026
328 pages
E-Book
978-1-040-96301-2 (ISBN)
Description
Kirchhoff Equations: A Variational Approach is primarily focussed on recent results concerning existence, multiplicity and the asymptotic behaviour of solutions to some stationary Kirchhoff problems, involving fractional integro-differential elliptic operators, and presenting difficulties relating to an intrinsic lack of compactness, which are elucidated upon within the text. These operators appear in a quite natural way in many different applications, such as, continuum mechanics, phase transition phenomena, population dynamics and game theory, as they are the typical outcome of stochastically stabilization of Levy processes.
This book will be of interest to postgraduates in applied mathematics, with a particular emphasis for those working in differential and partial differential equations. It will also find an audience among researchers interested in the qualitative, quantitative and asymptotic analysis of various types of solutions to the Kirchhoff equation.
Features
* Each chapter concludes with a detailed glossary and set of open problems.
* Rigorous proofs and illustrative examples.
* Broad-spectrum appeal to both applied mathematicians and those in other qualitative disciplines such as engineering.
This book will be of interest to postgraduates in applied mathematics, with a particular emphasis for those working in differential and partial differential equations. It will also find an audience among researchers interested in the qualitative, quantitative and asymptotic analysis of various types of solutions to the Kirchhoff equation.
Features
* Each chapter concludes with a detailed glossary and set of open problems.
* Rigorous proofs and illustrative examples.
* Broad-spectrum appeal to both applied mathematicians and those in other qualitative disciplines such as engineering.
More details
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
1 Tables, black and white
ISBN-13
978-1-040-96301-2 (9781040963012)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
approx. 08/2026
1st Edition
CRC Press
€142.50
Not yet published
Person
Vicentiu D. R?dulescu was a Distinguished Visiting Scientist at the University of Ljubljana (2008), Distinguished Adjunct Professor at the King Abdulaziz University in Jeddah (2014-2021), and Highly Cited Researcher (2014, 2019-2021). He is a member of the Accademia Peloritana dei Pericolanti (since 2014), Accademia delle Scienze dell'Umbria (since 2017), Senior Research Fellow of the City University of Hong Kong (2015), and Senior Research Fellow of the Central South University (2024 and 2025). He has editorial positions at the De Gruyter Series in Nonlinear Analysis and Applications, Journal of Geometric Analysis, Mathematical Methods in the Applied Sciences, Asymptotic Analysis, Complex Variables and Elliptic Equations, and Rendiconti del Circolo Matematico di Palermo. Vicentiu D. R?dulescu is also Editor-in-Chief of Bulletin of Mathematical Sciences, Opuscula Mathematica, and Boundary Value Problems.
Content
Chapter 1: Critical Kirchhoff Problems with Logarithmic Reaction.
Chapter 2: Planar Kirchhoff Equations with Critical Exponential Growth.
Chapter 3: Non-autonomous Kirchhoff Problems.
Chapter 4: Autonomous Kirchhoff Equations with Sobolev Critical Exponent.
Chapter 5: Kirchhoff Equations with Double-Behaviour Reaction.
Chapter 6: Fractional p-Kirchhoff Equations.
Chapter 7: Magnetic Kirchhoff Equations with Critical Growth.
Chapter 8: Fractional Kirchhoff Equations with Discontinuous Reaction.
Chapter 9: Mass Critical Fractional Kirchhoff Equations.
Appendix A: Fractional Sobolev Spaces.
Appendix B: Basic Inequalities and Theorems.
Bibliography.
Index.
Chapter 2: Planar Kirchhoff Equations with Critical Exponential Growth.
Chapter 3: Non-autonomous Kirchhoff Problems.
Chapter 4: Autonomous Kirchhoff Equations with Sobolev Critical Exponent.
Chapter 5: Kirchhoff Equations with Double-Behaviour Reaction.
Chapter 6: Fractional p-Kirchhoff Equations.
Chapter 7: Magnetic Kirchhoff Equations with Critical Growth.
Chapter 8: Fractional Kirchhoff Equations with Discontinuous Reaction.
Chapter 9: Mass Critical Fractional Kirchhoff Equations.
Appendix A: Fractional Sobolev Spaces.
Appendix B: Basic Inequalities and Theorems.
Bibliography.
Index.
