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Maximum Principles for the Hill's Equation
1st Edition
Authors:
Alberto Cabada
José Ángel Cid
Lucía López-Somoza
eBook ISBN: 9780128041260
Paperback ISBN: 9780128041178
Imprint: Academic Press
Published Date: 19th October 2017
Page Count: 252
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
- 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
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
1. Introduction
2. Homogeneous Equation
3. Non Homogeneous Equation
4. Nonlinear Equations
Appendix: Sobolev Inequalities
Details
- No. of pages:
- 252
- Language:
- English
- Copyright:
- © Academic Press 2018
- Published:
- 19th October 2017
- Imprint:
- Academic Press
- eBook ISBN:
- 9780128041260
- Paperback ISBN:
- 9780128041178
About the Author
Alberto Cabada
Alberto Cabada is Professor at the University of Santiago de Compostela (Spain). His line of research is devoted to the existence and multiplicity of solutions of nonlinear differential equations, both ordinary and partial, as well as difference and fractional ones. He is the author of more than one hundred forty research articles indexed in the Citation Index Report and has authored two monographs.
Affiliations and Expertise
Department of Mathematical Analysis, Faculty of Mathematics, Universidade de Santiago de Compostela
José Ángel Cid
José Ángel Cid is Associate Professor at the Universtity of Vigo (Spain). His main line of research is the qualitative analysis of boundary and initial value problems for ordinary differential equations. He is the author or co-author of more than forty research papers.
Affiliations and Expertise
Department of Mathematics, Campus de Ourense, Universidade de Vigo
Lucía López-Somoza
Lucía López-Somoza is a Ph.D. student at University of Santiago de Compostela (Spain). Her research is focused on the study of nonlinear functional differential equations.
Affiliations and Expertise
Department of Mathematical Analysis, Faculty of Mathematics, Universidade de Santiago de Compostela
Reviews
"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
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