Kirchhoff Equations

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 L©vy 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.

VicenÅ£iu D. RÇdulescu is a Professor at the AGH University of Krakow, Brno University of Technology and Professorial Fellow at the Simion Stoilow Institute of Mathematics of the Romanian Academy. He was also a Distinguished Visiting Scientist at the University of Ljubljana (2008), Distinguished Adjunct Professor at the King Abdulaziz University in Jeddah (2014â"2021), and Highly Cited Researcher (2014, 2019â"2021). He is a member of the Accademia Peloritana dei Pericolanti (since 2014), Accademia delle Scienze dellâUmbria (since 2017), Senior Research Fellow of the City University of Hong Kong (2015), and Senior Research Fellow of the Central South University (2024-2026). 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. VicenÅ£iu D. RÇdulescu is also Editor-in-Chief of Bulletin of Mathematical Sciences, Opuscula Mathematica, and Boundary Value Problems.