EAN: 9783319252872

SPRINGERBRIEFS IN MATHEMATICS A VARIATIONAL A...

This book highlights the current state of Lyapunov-type inequalities through a detailed
analysis. Aimed toward researchers and students working in differential equations and those
interested in the applications of stability theory and resonant systems  the book begins with
an overview Lyapunov's original results and moves forward to include prevalent results obtained
in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for
different boundary conditions for ordinary differential equations  including Neumann  Dirichlet
periodic  and antiperiodic conditions. Novel results of higher eigenvalues  systems of
equations  partial differential equations as well as variational approaches are presented. To
this respect  a new and unified variational point of view is introduced for the treatment of
such problems and a systematic discussion of different types of boundary conditions is
featured. Various problems make the study of Lyapunov-type inequalities of interest to those in
pure and applied mathematics. Originating with the study of the stability properties of the
Hill equation  other questions arose for instance in systems at resonance  crystallography 
isoperimetric problems  Rayleigh type quotients and oscillation and intervals of disconjugacy
and it lead to the study of Lyapunov-type inequalities for differential equations. This
classical area ofmathematics is still of great interest and remains a source of inspiration.

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