This book provides an extensive survey on Lyapunov-type inequalities. It
summarizes and puts order into a vast literature available on the
subject, and sketches recent developments in this topic. In an elegant
and didactic way, this work presents the concepts underlying
Lyapunov-type inequalities, covering how they developed and what kind of
problems they address.
This survey starts by introducing basic applications of Lyapunov's
inequalities. It then advances towards even-order, odd-order, and
higher-order boundary value problems; Lyapunov and Hartman-type
inequalities; systems of linear, nonlinear, and quasi-linear
differential equations; recent developments in Lyapunov-type
inequalities; partial differential equations; linear difference
equations; and Lyapunov-type inequalities for linear, half-linear, and
nonlinear dynamic equations on time scales, as well as linear
Hamiltonian dynamic systems.
Senior undergraduate students and graduate students of mathematics,
engineering, and science will benefit most from this book, as well as
researchers in the areas of ordinary differential equations, partial
differential equations, difference equations, and dynamic equations.
Some background in calculus, ordinary and partial differential
equations, and difference equations is recommended for full enjoyment of
the content.
