Maximum Principles for the Hill's Equation

Maximum Principles for the Hill's Equation

1st Edition - October 19, 2017

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  • Authors: Alberto Cabada, Jose Cid, Lucia Somoza
  • Paperback ISBN: 9780128041178
  • eBook ISBN: 9780128041260

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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

Product details

  • No. of pages: 252
  • Language: English
  • Copyright: © Academic Press 2017
  • Published: October 19, 2017
  • Imprint: Academic Press
  • Paperback ISBN: 9780128041178
  • eBook ISBN: 9780128041260

About the Authors

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

Jose 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

Lucia 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

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