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AuthorReid, William T. author
TitleSturmian Theory for Ordinary Differential Equations [electronic resource] / by William T. Reid
ImprintNew York, NY : Springer New York, 1980
Connect tohttp://dx.doi.org/10.1007/978-1-4612-6110-0
Descript XVI, 560 p. online resource

CONTENT

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


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