Maximum Principles for the Hill's Equation

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Language: English

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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

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.

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.
  • 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