Sturmian Theory for Ordinary Differential Equations - Livres de poche

EAN (ISBN-13): 9780387905426
ISBN (ISBN-10): 0387905421
Version reliée
Livre de poche
Date de parution: 1981
Editeur: Springer New York
584 Pages
Poids: 0,807 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2008-05-19T05:35:51+02:00 (Zurich)
Page de détail modifiée en dernier sur 2024-03-06T13:14:01+01:00 (Zurich)
ISBN/EAN: 9780387905426

ISBN - Autres types d'écriture:
0-387-90542-1, 978-0-387-90542-6
Autres types d'écriture et termes associés:
Auteur du livre: reid william, william burns, herdman
Titre du livre: equation, sturmian theory for ordinary differential equations, something out the ordinary, applied differential equations

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Données de l'éditeur

Auteur: William T. Reid
Titre: Applied Mathematical Sciences; Sturmian Theory for Ordinary Differential Equations
Editeur: Springer; Springer US
560 Pages
Date de parution: 1981-02-20
New York; NY; US
Langue: Anglais
53,49 € (DE)
54,99 € (AT)
59,00 CHF (CH)
Available
XVI, 560 p.

BC; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Equations; Hilbert space; Sturmsche Theorie; differential equation; ordinary differential equation; Analysis; EA

I. Historical Prologue.- 1. Introduction.- 2. Methods Based Upon Variational Principles.- 3. Historical Comments on Terminology.- II. Sturmian Theory for Real Linear Homogeneous Second Order Ordinary Differential Equations on a Compact Interval.- 1. Introduction.- 2. Preliminary Properties of Solutions of (1.1).- 3. The Classical Oscillation and Comparison Theorems of Sturm.- 4. Related Oscillation and Comparison Theorems.- 5. Sturmian Differential Systems.- 6. Polar Coordinate Transformations.- 7. Transformations for Differential Equations and Systems.- 8. Variational Properties of Solutions of (1.1).- 9. Comparison Theorems.- 10. Morse Fundamental Quadratic Forms for Conjugate and Focal Points.- 11. Survey of Recent Literature.- 12. Topics and Exercises.- III. Self-Adjoint Boundary Problems Associated with Second Order Linear Differential Equations.- 1. A Canonical Form for Boundary Conditions.- 2 Extremum Problems for Self-Adjoint Systems.- 3. Comparison Theorems.- 4. Comments on Recent Literature.- 5. Topics and Exercises.- IV. Oscillation Theory on a Non-Compact Interval.- 1. Introduction.- 2. Integral Criteria for Oscillation and Non-Oscillation.- 3. Principal Solutions.- 4. Theory of Singular Quadratic Functionals.- 5. Interrelations Between Oscillation Criteria and Boundary Problems.- 6. Strong and Conditional Oscillation.- 7. A Class of Sturmian Problems on a Non-Compact Interval.- 8. Topics and Exercises.- V. Sturmian Theory for Differential Systems.- 1. Introduction.- 2. Special Examples.- 3. Preliminary Properties of Solutions of (2.5).- 4. Associated Riccati Matrix Differential Equations.- 5. Normality and Abnormality.- 6. Variational Properties of Solutions of (3.1).- 7. Comparison Theorems.- 8. Morse Fundamental Hermitian Forms.- 9. Generalized Polar Coordinate Transformations for Matrix Differential Systems.- 10. Matrix Oscillation Theory.- 11. Principal Solutions.- 12. Comments on Systems (3.1) Which are Not Identically Normal.- 13. Comments on the Literature on Oscillation Theory for Hamiltonian Systems (3.1).- 14. Higher Order Differential Equations.- 15. Topics and Exercises.- VI. Self-Adjoint Boundary Problems.- 1. Introduction.- 2. Normality and Abnormality of Boundary Problems.- 3. Self-Adjoint Boundary Problems Associated with (B).- 4. Comparison Theorems.- 5. Treatment of Self-Adjoint Boundary Problems by Matrix Oscillation Theory.- 6. Notes and Comments on the Literature.- 7. Topics and Exercises.- VII. A Class of Definite Boundary Problems.- 1. Introduction.- 2. Definitely Self-Adjoint Boundary Problems.- 3. Comments on Related Literature.- 4. Topics and Exercises.- VIII. Generalizations of Sturmian Theory.- 1. Introduction.- 2. Integro-Differential Boundary Problems.- 3. A Class of Generalized Differential Equations.- 4. Hestenes Quadratic Form Theory in a Hilbert Space.- 5. The Weinstein Method of Intermediate Problems.- 6. Oscillation Phenomena for Hamiltonian Systems in a B*-Algebra.- 7. Topological Interpretations of the Sturmian Theorems.- Abbreviations for Mathematical Publications Most Frequently Used.- Special Symbols.- Author Index.