Maximum Principles for the Hill's Equation
- 1st Edition - October 19, 2017
- Latest edition
- Authors: Alberto Cabada, José Ángel Cid, Lucía López-Somoza
- Language: English
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-P… Read more
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Description
Description
Maximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,…) and for problems with parametric dependence. The authors discuss the properties of the related Green’s functions coupled with different boundary value conditions. In addition, they establish the equations’ relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included.
Key features
Key features
- Evaluates classical topics in the Hill’s equation that are crucial for understanding modern physical models and non-linear applications
- Describes explicit and effective conditions on maximum and anti-maximum principles
- Collates information from disparate sources in one self-contained volume, with extensive referencing throughout
Readership
Readership
Trained mathematicians, including both theoretical and applied mathematicians working on the subject of differential equations. The book also could be used for a Ph. D course addressed to graduate students
Table of contents
Table of contents
1. Introduction 2. Homogeneous Equation3. Non Homogeneous Equation4. Nonlinear EquationsAppendix: Sobolev Inequalities
Review quotes
Review quotes
"The book presents a deep and up-to-date theory on the Hill’s equation. It is well organized, by giving a rich list of references at the end of each chapter, as well as, a sufficient number of illustrative examples. It is easily readable by mathematicians working on the field of ordinary differential equations and, certainly, it could be recommended as a good guide for a related graduate course."—Zentralblatt Math
"This volume will be useful for a wide range of mathematicians, including graduate students and researchers interested in the theory and applications of second-order ordinary differential equations, especially Hill type equations (which are still a hot topic at present) and also nonlinear equations, equations with singularities and parameters. The theorems are carefully proved, and in each chapter an adequate list of references is given. Finally, the book contains many explanatory remarks and examples which may contribute to a better understanding of the theoretical results."—Mathematical Reviews Clippings
"This volume will be useful for a wide range of mathematicians, including graduate students and researchers interested in the theory and applications of second-order ordinary differential equations, especially Hill type equations (which are still a hot topic at present) and also nonlinear equations, equations with singularities and parameters. The theorems are carefully proved, and in each chapter an adequate list of references is given. Finally, the book contains many explanatory remarks and examples which may contribute to a better understanding of the theoretical results."—MathSciNet
Product details
Product details
- Edition: 1
- Latest edition
- Published: October 19, 2017
- Language: English
About the authors
About the authors
AC
Alberto Cabada
JC
José Ángel Cid
LL