Handbook of Nonconvex Analysis and Applications [

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Nonconvex analysis is a rapidly developing, multi-disciplinary field of research, comprehending theoretical analysis in mathematical modelling of natural systems, bifurcation and chaos in dynamical systems, finite deformation theory, nonlinear partial differential equations, global optimization, calculus of variation, numerical methods, and scientific computations. The field of nonconvex analysis has undergone considerable development in a remarkably short time -- with extensive applications to theoretical physics, material science, modern mechanics, complex systems, and scientific computations. The present volume, Handbook of Nonconvex Analysis and Applications, consists of thirteen chapters written by notable experts in the field, addressing essential recent developments in nonconvex analysis and its applications, and keeping a balance between major areas of theory, methods, and applications. Each chapter provides an illuminating exposition of state-of-the-art approaches to a specific topic, with discussions of the central contributions, and pointers to some basic references. A variety of topics regarding nonconvex analysis and its applications are discussed: nonconvex variational principles; comparison principles; nonlinear eigenvalue problems; critical point theory; boundary value problems; topological methods, including Morse theory; nonlinear elliptic equations; evolution problems; difference equations; inequality problems; geometric properties of functions and spaces; and applications in mechanics. This Handbook will serve as a much-needed reference work for the dynamic and ever-growing field of nonconvex analysis and its applications.

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David Yang Gao is Alexander Rubinov Professor of Mathematics in the Graduate School of Information Technology and Mathematical Sciences at the University of Ballarat, Australia. He has published ten books and more than 150 papers on applied mathematics, mechanics, operations research, and computational science. His research interest has been focused on duality theory and methods in nonconvex systems with applications in engineering and sciences. -- Dumitru Motreanu is Professor of Mathematics at the University of Perpignan, France. He co-authored six monographs and more than 170 research articles in the fields of nonlinear analysis, partial differential equations and optimization. His current work concerns nonlinear elliptic equations, spectral problems and variational methods.