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Publisher:

Dover Publications

Publication Date:

2009

Number of Pages:

361

Format:

Paperback

Price:

19.95

ISBN:

9780486472119

Category:

Textbook

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

We do not plan to review this book.

MATHEMATICAL PRELIMINARIES | |||||||

Banach spaces and examples | |||||||

Linear transformations | |||||||

Fixed point theorems | |||||||

GENERAL PROPERTIES OF DIFFERENTIAL EQUATIONS | |||||||

Existence | |||||||

Continuation of solutions | |||||||

Uniqueness and continuity properties | |||||||

Continuous dependence and stability | |||||||

Extension of the concept of a differential equation | |||||||

Differential inequalities | |||||||

Autonomous systems-generalities | |||||||

Autonomous systems-limit sets, invariant sets | |||||||

Remarks and suggestions for further study | |||||||

TWO DIMENSIONAL SYSTEMS | |||||||

Planar two dimensional systems-the Poincaré-Bendixson theory | |||||||

Differential systems on a torus | |||||||

Remarks and suggestions for further study | |||||||

LINEAR SYSTEMS AND LINEARIZATION | |||||||

General linear systems | |||||||

Stability of linear and perturbed linear systems | |||||||

nth Order scalar equations | |||||||

Linear systems with constant coefficients | |||||||

Two dimensional linear autonomous systems | |||||||

The saddle point property | |||||||

Linear periodic systems | |||||||

Hill’s equation | |||||||

Reciprocal systems | |||||||

Canonical systems | |||||||

Remarks and suggestion for further study | |||||||

PERTURBATION OF NONCRITICAL LINEAR SYSTEMS | |||||||

Nonhomogeneous linear systems | |||||||

Weakly nonlinear equations-noncritical case | |||||||

The general saddle point property | |||||||

More general systems | |||||||

The Duffing equation with large damping and large forcing | |||||||

Remarks and extensions | |||||||

SIMPLE OSCILLATORY PHENOMENA AND THE METHOD OF AVERAGING | |||||||

Conservative systems | |||||||

Nonconservative second order equations-limit cycles | |||||||

Averaging | |||||||

The forced van der Pol equation | |||||||

Duffing’s equation with small damping and small harmonic forcing | |||||||

The subharmonic of order 3 for Duffing’s equation | |||||||

Damped excited pendulum with oscillating support | |||||||

Exercises | |||||||

Remarks and suggestions for further study | |||||||

BEHAVIOR NEAR A PERIODIC ORBIT | |||||||

Stability of a periodic orbit | |||||||

Sufficient conditions for orbital stability in two dimensions | |||||||

Autonomous perturbations | |||||||

Remarks and suggestions for further study | |||||||

INTEGRAL MANIFOLDS OF EQUATIONS WITH A SMALL PARAMETER | |||||||

Methods of determining integral manifolds | |||||||

Statement of results | |||||||

A “nonhomgeneous linear” system | |||||||

The mapping principle | |||||||

Proof of Theorem 2.1 | |||||||

Stability of the perturbed manifold | |||||||

Applications | |||||||

Exercises | |||||||

Remarks and suggestions for further study | |||||||

PERIODIC SYSTEMS WITH A SMALL PARAMETER | |||||||

A special system of equations | |||||||

Almost linear systems | |||||||

Periodic solutions of perturbed autonomous equa | |||||||

Remarks and suggestions for further study | |||||||

ALTERNATIVE PROBLEMS FOR THE SOLUTION OF FUNCTIONAL EQUATIONS | |||||||

Equivalent equations | |||||||

A generalization | |||||||

Alternative problems | |||||||

Alternative problems for periodic solutions | |||||||

The Perron-Lettenmeyer theorem | |||||||

Remarks and suggestions for further study | |||||||

THE DIRECT METHOD OF LIAPUNOV | |||||||

Sufficient conditions for stability and instability in autonomous systems | |||||||

Circuits containing Esaki diodes | |||||||

Sufficient conditions for stability in nonautonomous systems | |||||||

The converse theorems for asymptotic stability | |||||||

Implications of asymptotic stability | |||||||

Wazewski’s principle | |||||||

Remarks and suggestions for further study | |||||||

APPENDIX | |||||||

ALMOST PERIODIC FUNCTIONS | |||||||

REFERENCES | |||||||

INDEX |

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