LEADER 03624nam 2200613 450 001 9910819073203321 005 20200811234409.0 010 $a1-4704-1056-7 035 $a(CKB)3780000000000271 035 $a(EBL)3114096 035 $a(SSID)ssj0000938807 035 $a(PQKBManifestationID)11514762 035 $a(PQKBTitleCode)TC0000938807 035 $a(PQKBWorkID)10925965 035 $a(PQKB)11154781 035 $a(MiAaPQ)EBC3114096 035 $a(RPAM)17765954 035 $a(PPN)195408403 035 $a(EXLCZ)993780000000000271 100 $a20150417h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOn some aspects of oscillation theory and geometry /$fBruno Bianchini, Luciano Mari, Marco Rigoli 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2012. 210 4$dİ2012 215 $a1 online resource (208 p.) 225 1 $aMemoirs of the American Mathematical Society,$x1947-6221 ;$vVolume 225, Number 1056 300 $a"Volume 225, Number 1056 (first of 4 numbers)." 311 $a0-8218-8799-8 320 $aIncludes bibliographical references. 327 $a""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 ( a???)a???+ =0"" 327 $a""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 -I??- ( ) 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"" 327 $a""6.3. Instability and index of -I??- ( )""""6.4. Some remarks on minimal surfaces""; ""6.5. Newton operators, unstable hypersurfaces and the Gauss map""; ""6.6. Dealing with a possibly negative potential""; ""6.7. An extension of Calabi compactness criterion""; ""Chapter 7. Much above the critical curve""; ""7.1. Controlling the oscillation""; ""7.2. The growth of the index of -I??- ( )""; ""7.3. The essential spectrum of -I?? and punctured manifolds""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 225, Number 1056. 606 $aDifference equations$xOscillation theory 606 $aSpectral theory (Mathematics) 606 $aDifferential equations, Elliptic 615 0$aDifference equations$xOscillation theory. 615 0$aSpectral theory (Mathematics) 615 0$aDifferential equations, Elliptic. 676 $a515.352 700 $aBianchini$b Bruno$f1958-$01124954 702 $aMari$b Luciano$f1983- 702 $aRigoli$b Marco 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819073203321 996 $aOn some aspects of oscillation theory and geometry$93999469 997 $aUNINA