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Maximum Principles for the Hill's Equation de Alberto Cabada

Maximum Principles for the Hill's Equation

Autor Alberto Cabada, José Ángel Cid, Lucía López-Somoza
en Limba Engleză Paperback – 19 oct 2017
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.


  • 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
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Specificații

ISBN-13: 9780128041178
ISBN-10: 012804117X
Pagini: 252
Dimensiuni: 152 x 229 x 16 mm
Greutate: 0.41 kg
Editura: ELSEVIER SCIENCE

Public țintă

The primary audience will consist of 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. This audience will benefit from a short book providing both complete and accessible information of classical results and recent developments related to the subject.

Cuprins

1. Introduction 2. Homogeneous Equation3. Non Homogeneous Equation4. Nonlinear EquationsAppendix: Sobolev Inequalities

Recenzii

"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