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

Format:

Book

Author/Creator:

Bianchini, Bruno, 1958- author.

Mari, Luciano, 1983- author.

Rigoli, Marco, author.

Series:

Memoirs of the American Mathematical Society ; Volume 225, Number 1056.

Memoirs of the American Mathematical Society, 1947-6221 ; Volume 225, Number 1056

Language:

English

Subjects (All):

Difference equations--Oscillation theory.

Difference equations.

Spectral theory (Mathematics).

Differential equations, Elliptic.

Physical Description:

1 online resource (208 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2012.

Language Note:

English

Summary:

September 2013, volume 225, number 1056 (first of 4 numbers).

Contents:

""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 ( �)�+ =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""

Notes:

"Volume 225, Number 1056 (first of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-1056-7