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A Variational Approach to Lyapunov Type Inequalities: From ODEs to PDEs

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 of

mathematics is still of great interest and remains a source of inspiration.

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Detail Information
Series Title
SpringerBriefs in Mathematics
Call Number
515.4 CAN v
Publisher
Cham : Springer.,
Collation
XVIII, 120
Language
English
ISBN/ISSN
978-3-319-25289-6
Classification
515.4
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
Ed. 1
Subject(s)
Differential equations
Integral Transforms and Operational Calculus
Specific Detail Info
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Statement of Responsibility
Other Information
Cataloger
umi
Source
https://link.springer.com/content/pdf/10.1007/978-3-319-25289-6.pdf?pdf=button
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