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Catalogue Information
Field name	Details
Dewey Class	515.352
Title	A Variational Approach to Lyapunov Type Inequalities ([EBook]) : From ODEs to PDEs / / by Antonio Cañada, Salvador Villegas.
Author	Cañada, Antonio
Added Personal Name	Villegas, Salvador author.
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	XVIII, 120 p. : online resource.
Series	SpringerBriefs in Mathematics 2191-8198
ISBN	9783319252896
Summary Note	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. .:
Contents note	1. Introduction -- 2. A variational characterization of the best Lyapunov constants -- 3. Higher eigenvalues -- 4. Partial differential equations -- 5. Systems of equations -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-25289-6
Links to Related Works	Subject References: Difference and Functional Equations . Difference equations . Differential Equations . Functional equations . Integral transforms . Integral Transforms, Operational Calculus . Mathematics . Operational calculus . Ordinary differential equations . Partial differential equations . Authors: Cañada, Antonio . Villegas, Salvador . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 515.352 .

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

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