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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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