VII. The Applications of a Fixed Point Theorem to a Variety of Non-Linear Stability Problems

Kapitel in diesem Buch

1. Frontmatter i
2. Preface v
3. Contents vii
4. I. The Time Optimal Control Problem 1
5. II. Continuous Dependence on a Parameter 25
6. III. Poincare’s Perturbation Method and Topological Degree 37
7. IV. On the Behavior of the Solutions of Linear Periodic Differential Systems Near Resonance Points 55
8. V. On the Stability of Periodic Solutions of Weakly Nonlinear Periodic and Autonomous Differential Systems 91
9. VI. Existence Theorems for Periodic Solutions of Nonlinear Lipschitzian Differential Systems and Fixed Point Theorems 115
10. VII. The Applications of a Fixed Point Theorem to a Variety of Non-Linear Stability Problems 173
11. VIII. Quadratic Differential Equations and Non-Associative Algebras 185
12. IX. Sur Une Propriété De L’Ensemble Des Thajectoires Bornées De Certains Systèmes Dynamiques 215
13. X. On Lagrange Stable Motions in the Neighborhood of Critical Points 219
14. XI. The Local Theory of Piecewise Continuous Differential Equations 225
15. XII. Asymptotic Stability in 3-Space 257
16. XIII. Existence and Uniqueness of the Periodic Solution of an Equation for Autonomous Oscillations 269
17. Appendix 285