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 Lévy 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.
