Maximum principles for the Hill's equation [[Recurso electrónico] /] / Alberto Cabada, Jose Angel Cid, Lucia Lopez-Somoza

• Autore: Cabada Alberto
• Pubblicazione: London, England : , : Academic Press, , 2018
• Descrizione fisica: 1 recurso electrónico (254 p.)
• Disciplina: 515.352
• Soggetto topico: Ecuación de Hill; Hill's equation
• Persona (resp. second.): CidJose Angel; Lopez SomozaLucia
• Nota di bibliografia: Incluye referencias bibliográficas al final de cada capítulo
• Nota di contenuto: Machine generated contents note: ; 1. Introduction -- ; 1.1. Hill's Equation -- ; 1.2. Stability in the Sense of Lyapunov -- ; 1.3. Floquet's Theorem for the Hill's Equation -- References -- ; 2. Homogeneous Equation -- ; 2.1. Introduction -- ; 2.2. Sturm Comparison Theory -- ; 2.3. Spectral Properties of Dirichlet Problem -- ; 2.4. Spectral Properties of Mixed and Neumann Problems -- ; 2.5. Spectral Properties of the Periodic Problem: Intervals of Stability and Instability -- ; 2.6. Relation Between Eigenvalues of Neumann, Dirichlet, Periodic, and Antiperiodic Problems -- References -- ; 3. Nonhomogeneous Equation -- ; 3.1. Introduction -- ; 3.2. The Green's Function -- ; 3.3. Periodic Conditions -- ; 3.3.1. Properties of the Periodic Green's Function -- ; 3.3.2. Optimal Conditions for the Periodic MP and AMP -- ; 3.3.3. Explicit Criteria for the Periodic AMP and MP -- ; 3.3.4. More on Explicit Criteria -- ; 3.3.5. Examples -- ; 3.4. Non-Periodic Conditions -- ; 3.4.1. Neumann Problem -- ; 3.4.2. Dirichlet Problem -- ; 3.4.3. Relation Between Neumann and Dirichlet Problems -- ; 3.4.4. Mixed Problems and their Relation with Neumann and Dirichlet Ones -- ; 3.4.5. Order of Eigenvalues and Constant Sign of the Green's Function -- ; 3.4.6. Relations Between Green's Functions. Comparison Principles -- ; 3.4.7. Constant Sign for Non-Periodic Green's Functions -- ; 3.4.8. Global Order of Eigenvalues -- ; 3.4.9. Examples -- ; 3.5. General Second Order Equation -- ; 3.5.1. Periodic Problem -- ; 3.5.2. Non-Periodic Conditions -- References -- ; 4. Nonlinear Equations -- ; 4.1. Introduction -- ; 4.2. Fixed Point Theorems and Degree Theory -- ; 4.2.1. Leray-Schauder Degree -- ; 4.2.2. Fixed Point Theorems -- ; 4.2.3. Extremal Fixed Points -- ; 4.2.4. Monotone Operators -- ; 4.2.5. Non-increasing Operators -- ; 4.2.6. Non-decreasing Operators -- ; 4.2.7. Problems with Parametric Dependence -- ; 4.3. Lower and Upper Solutions Method -- ; 4.3.1. Well Ordered Lower and Upper Solutions -- ; 4.3.2. Existence of Extremal Solutions -- ; 4.3.3. Non-Well-Ordered Lower and Upper Solutions -- ; 4.4. Monotone Iterative Techniques -- ; 4.4.1. Well Ordered Lower and Upper Solutions -- ; 4.4.2. Reversed Ordered Lower and Upper Solutions -- References.
• Sommario/riassunto: 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.--
• Titolo autorizzato: Maximum principles for the Hill's equation
• ISBN: 0-12-804126-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910583381303321
• Lo trovi qui: Univ. Federico II