This book systematically introduces the theory of nonlinear
analysis, providing an overview of topics such as geometry of
Banach spaces, differential calculus in Banach spaces, monotone
operators, and fixed point theorems. It also discusses degree
theory, nonlinear matrix equations, control theory, differential
and integral equations, and inclusions. The book presents
surjectivity theorems, variational inequalities, stochastic game
theory and mathematical biology, along with a large number of
applications of these theories in various other disciplines.
Nonlinear analysis is characterised by its applications in numerous
interdisciplinary fields, ranging from engineering to space
science, hydromechanics to astrophysics, chemistry to biology,
theoretical mechanics to biomechanics and economics to stochastic
game theory. Organised into ten chapters, the book shows the
elegance of the subject and its deep-rooted concepts and
techniques, which provide the tools for developing more realistic
and accurate models for a variety of phenomena encountered in
diverse applied fields. It is intended for graduate and
undergraduate students of mathematics and engineering who are
familiar with discrete mathematical structures, differential and
integral equations, operator theory, measure theory, Banach and
Hilbert spaces, locally convex topological vector spaces, and
linear functional analysis.
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