Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations.
Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.
1. 8.1 Introduction - p. page287 2. 8.2 Method of steps - p. 289 3. 8.3 Existence and uniqueness - p. 292 4. 8.4 Stability using Lyapunov functions - p. 299 5. 8.5 Stability using fixed point theory - p. 298 6. 8.6 Exponential stability - p. 309 7. 8.7 Existence of positive periodic solutions - p. 319 8. 8.8 Exercises - p. 326 9. Bibliography - p. 328 10. Chapter 9. New variation of parameters - p. 329 11. Bibliography - p. 343 12. Index - p. 347
Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations.
Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.
1. 8.1 Introduction - p. page287 2. 8.2 Method of steps - p. 289 3. 8.3 Existence and uniqueness - p. 292 4. 8.4 Stability using Lyapunov functions - p. 299 5. 8.5 Stability using fixed point theory - p. 298 6. 8.6 Exponential stability - p. 309 7. 8.7 Existence of positive periodic solutions - p. 319 8. 8.8 Exercises - p. 326 9. Bibliography - p. 328 10. Chapter 9. New variation of parameters - p. 329 11. Bibliography - p. 343 12. Index - p. 347
