A Variational Approach to Lyapunov Type Inequalities

From ODEs to PDEs

Nonfiction, Science & Nature, Mathematics, Differential Equations, Mathematical Analysis
Cover of the book A Variational Approach to Lyapunov Type Inequalities by Antonio Cañada, Salvador Villegas, Springer International Publishing
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Author: Antonio Cañada, Salvador Villegas ISBN: 9783319252896
Publisher: Springer International Publishing Publication: November 24, 2015
Imprint: Springer Language: English
Author: Antonio Cañada, Salvador Villegas
ISBN: 9783319252896
Publisher: Springer International Publishing
Publication: November 24, 2015
Imprint: Springer
Language: English

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.

 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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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