03624nam 2200613 450 991081907320332120200811234409.01-4704-1056-7(CKB)3780000000000271(EBL)3114096(SSID)ssj0000938807(PQKBManifestationID)11514762(PQKBTitleCode)TC0000938807(PQKBWorkID)10925965(PQKB)11154781(MiAaPQ)EBC3114096(RPAM)17765954(PPN)195408403(EXLCZ)99378000000000027120150417h20122012 uy 0engur|n|---|||||txtccrOn some aspects of oscillation theory and geometry /Bruno Bianchini, Luciano Mari, Marco RigoliProvidence, Rhode Island :American Mathematical Society,2012.©20121 online resource (208 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 225, Number 1056"Volume 225, Number 1056 (first of 4 numbers)."0-8218-8799-8 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Volume 225, Number 1056.Difference equationsOscillation theorySpectral theory (Mathematics)Differential equations, EllipticDifference equationsOscillation theory.Spectral theory (Mathematics)Differential equations, Elliptic.515.352Bianchini Bruno1958-1124954Mari Luciano1983-Rigoli MarcoMiAaPQMiAaPQMiAaPQBOOK9910819073203321On some aspects of oscillation theory and geometry3999469UNINA