Maximum Principles for the Hill's Equation

ISBN-13: 9780128041178 / Angielski / Miękka / 2017 / 252 str.

Faculty of Mathe Lucia (Department of Mathematical Analysis

Opis

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

Recenzje

"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

Spis treści

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

O autorze

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. 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. 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.