On some aspects of oscillation theory and geometry / / Bruno Bianchini, Luciano Mari, Marco Rigoli

• Autore: Bianchini Bruno <1958->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2012; ©2012
• Descrizione fisica: 1 online resource (208 p.)
• Disciplina: 515.352
• Soggetto topico: Difference equations - Oscillation theory; Spectral theory (Mathematics); Differential equations, Elliptic
• Persona (resp. second.): MariLuciano <1983->; RigoliMarco
• Note generali: "Volume 225, Number 1056 (first of 4 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. The Geometric setting""; ""2.1. Cut-locus and volume growth function""; ""2.2. Model manifolds and basic comparisons""; ""2.3. Some spectral theory on manifolds""; ""Chapter 3. Some geometric examples related to oscillation theory""; ""3.1. Conjugate points and Myers type compactness results""; ""3.2. The spectrum of the Laplacian on complete manifolds""; ""3.3. Spectral estimates and immersions""; ""3.4. Spectral estimates and nonlinear PDE""; ""Chapter 4. On the solutions of the ODE ( â€?)â€?+ =0"" ; ""4.1. Existence, uniqueness and the behaviour of zeroes""""4.2. The critical curve: definition and main estimates""; ""Chapter 5. Below the critical curve""; ""5.1. Positivity and estimates from below""; ""5.2. Stability, index of -Î?- ( ) and the uncertainty principle""; ""5.3. A comparison at infinity for nonlinear PDE""; ""5.4. Yamabe type equations with a sign-changing nonlinearity""; ""5.5. Upper bounds for the number of zeroes of ""; ""Chapter 6. Exceeding the critical curve""; ""6.1. First zero and oscillation""; ""6.2. Comparison with known criteria"" ; ""6.3. Instability and index of -Î?- ( )""""6.4. Some remarks on minimal surfaces""; ""6.5. Newton operators, unstable hypersurfaces and the Gauss map""; ""6.6. Dealing with a possibly negative potential""; ""6.7. An extension of Calabi compactness criterion""; ""Chapter 7. Much above the critical curve""; ""7.1. Controlling the oscillation""; ""7.2. The growth of the index of -Î?- ( )""; ""7.3. The essential spectrum of -Î? and punctured manifolds""; ""Bibliography""
• Titolo autorizzato: On some aspects of oscillation theory and geometry
• ISBN: 1-4704-1056-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910819073203321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 225, Number 1056.