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Maximum Principles for the Hill's Equation
Provides classical and modern assessment of the Hill’s equation in its homogenous and non-homogenous states
Alberto Cabada (Author), José Ángel Cid (Author), Lucía López-Somoza (Author)
9780128041178
Paperback, published 19 October 2017
252 pages
22.9 x 15.1 x 1.7 cm, 0.41 kg
"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
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.
1. Introduction 2. Homogeneous Equation3. Non Homogeneous Equation4. Nonlinear EquationsAppendix: Sobolev Inequalities
Subject Areas: Applied mathematics [PBW]
