Maximum Principles for the Hills Equation

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 applicationsDescribes explicit and effective conditions on maximum and anti-maximum principlesCollates information from disparate sources in one self-contained volume, with extensive referencing throughout INDICE: 1. Introduction 1.1. Hill's equation 1.2. Stability in the sense of Lyapunov 2. Homogeneous equation 2.1. Introduction 2.2. Sturm comparison theory. 2.3. Spectral properties of the Dirichlet Problem. 2.4. Spectral properties of the Periodic Problem: intervals of stability and instability 3. Non homogeneous equation 3.1. Introduction 3.2. The Green's function 3.3. Some spectral characterizations for the Maximum and Anti-Maximum principles 3.4. Explicit conditions for the Maximum and Anti-Maximum principles 4. Nonlinear equations 4.1. Lower and upper solutions 4.2. Monotone iterative techniques 4.3. Fixed points for positive operators 4.4. Problems with singularities 4.5. Problems with parametric dependence 5. Appendix 5.1. Floquet theory 5.2. Sobolev Inequalities

• ISBN: 978-0-12-804117-8
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 160
• Fecha Publicación: 01/10/2017
• Nº Volúmenes: 1
• Idioma: Inglés