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| Critical Extremals | |
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| Minimizing Extremals g: Fixed Endpoints | |
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| The Euler Equations | |
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| The Existence of Extremals Near g | |
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| The Necessary Conditions of Weierstrass and Legendre | |
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| The Jacobi Condition | |
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| Conjugate Points in the Nonsingular Case | |
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| The Hilbert Integral | |
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| Sufficient Conditions | |
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| The Algebraic Index of a Critical Extremal g | |
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| General End Conditions C[subscript r], Locally Defined | |
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| C[subscript r]-Transversality Conditions on g | |
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| The Second Variation of (J,C[subscript r]), r > 0 | |
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| Critical Secondary Extremals: Endpoints Variable | |
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| Critical Secondary Extremals: Endpoints Fixed | |
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| Quadratic Index Forms, Derived and Free | |
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| Derived Index Forms | |
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| The Framed Family [Gamma superscript lambda] of Broken [lambda]-Extremals | |
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| The "Geometric" Index of a Critical Extremal g | |
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| Free Index Forms | |
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| Free Linear Differential and Boundary Conditions | |
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| Relative Minima under General End Conditions C[subscript r] | |
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| Focal Conditions and Sturm-Like Theorems | |
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| The Focal Point Theorem | |
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| Focal Conditions, Derived and Free | |
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| Conjugate Families (von Escherich) | |
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| Proof of Focal Point Theorem 17.3 | |
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| Sturm-Like Theorems in E[subscript m+1] | |
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| The Separation Theorem in E[subscript m+1] | |
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| Comparison of Free Focal Conditions | |
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| The Sturm Comparisons When m = 1 | |
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| The Variation of Conjugate Points | |
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| General Boundary Conditions | |
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| The Oscillation Number, Index W[subscript 0] | |
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| Conjugate Points and Characteristic Roots | |
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| The Auxiliary Theorem on Quadratic Forms | |
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| Proof of Oscillation Theorem 24.1 | |
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| Quadratic End Forms of the System W[subscript r] | |
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| A Minimizing Periodic Extremal g | |
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| Selfadjoint Boundary Conditions | |
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| General Mixed Boundary Conditions | |
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| Conditions for Selfadjointness | |
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| The Reduction of Selfadjoint BC to Canonical Form | |
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| Prestructures for Characteristic Root Theory | |
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| Admissible Canonical Systems W[subscript r] | |
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| The Dependence on [lambda] | |
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| Canonical Systems W[subscript r] | |
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| The Existence of Characteristic Roots | |
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| Selfconjugate Limit Values | |
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| Comparison of Characteristic Roots | |
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| The W[subscript r]-Nuclear Comparison Test | |
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| Oscillation Criteria | |
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| Free Linear Conditions | |
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| Free Second-Order Differential Equations | |
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| Solution of the Differential Equations (1.5) | |
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| Conjugate Points | |
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| Second-Order DE with a Parameter [alpha] | |
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| The End Space ((W[subscript r])) of W[subscript r] | |
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| Subordinate Quadratic Forms and Their Complementary Forms | |
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| Auxiliary Theorem 25.1 | |
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| The Case of a Nonsingular Form P(0,s) | |
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| Proof of Theorem 25.1 Completed | |
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| Model Families of Quadratic Forms | |
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| Model Families F | |
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| Model Families G | |
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| The Principal Theorem of Appendix III | |
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| References | |
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| Index | |