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XI. The Local Theory of Piecewise Continuous Differential Equations

  • J. André and P. Seibert
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Contributions to the Theory of Nonlinear Oscillations, Volume V
This chapter is in the book Contributions to the Theory of Nonlinear Oscillations, Volume V
© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  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
https://doi.org/10.1515/9781400882649-012

Chapters in this book

  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
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