Contributions to the theory of nonlinear oscillations

Author(s)

• Cartwright, Mary Lucy
• Diliberto, S. P.
• Cesari, Lamberto
• Seifert, G.
• Antosiewicz, H. A.
• Lefschetz, Solomon
• LaSalle, Joseph P.

Bibliographic Information

Contributions to the theory of nonlinear oscillations

edited by S. Lefschetz

（Annals of mathematics studies, no. 20, 29, 36, 41, 45）

Princeton University Press, 1950-1960

• [v. 1]
• v. 2
• v. 3
• v. 4
• v. 5

Note

Vol. 1 by S.P. Diliberto ... [et al.] ; edited by S. Lefschetz

Vol. 2 by M.L. Cartwright ... [et al.] ; edited by S. Lefschetz

Vol. 3 by G. Seifert ... [et al.] ; edited by S. Lefschetz

Vol. 4 by H. Antosiewicz ... [et al.] ; edited by S. Lefschetz

Vol. 5 by J.P. LaSalle ... [et al.] ; edited by L. Cesari, J. LaSalle, and S. Lefschez

Includes bibliographies

Description and Table of Contents

Volume

v. 3 ISBN 9780691079110

Description

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-36), Volume III, will be forthcoming.

Table of Contents

*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*I. A ROTATED VECTOR APPROACH TO THE PROBLEM OP STABILITY OP SOLUTIONS OF PENDULUM-TYPE EQUATIONS, pg. 1*II. ASYMPTOTICALLY AUTONOMOUS DIFFERENTIAL SYSTEMS, pg. 17*III. NONLINEAR DIFFERENTIAL EQUATIONS SYSTEMS, pg. 31*IV. ON A NON-LINEAR DIFFERENTIAL EQUATION CONTAINING A SMALL PARAMETER, pg. 57*V. CRITICAL POINTS AT INFINITY AND FORCED OSCILLATION, pg. 85*VI. ON CERTAIN CRITICAL POINTS OF A DIFFERENTIAL SYSTEM IN THE PLANE, pg. 127*VII. ON THE TOTAL NUMBER OF SINGULAR POINTS AND LIMIT CYCLES OF A DIFFERENTIAL EQUATION, pg. 137*VIII. BANACH SPACES AND THE PERTURBATION OF ORDINARY DIFFERENTIAL EQUATIONS, pg. 173*IX. A FIXED POINT THEOREM, pg. 197*X. PERTURBATION THEOREMS FOR NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS, pg. 207*XI. A NOTE ON THE EXISTENCE OF PERIODIC SOLUTIONS OF DIFFERENTIAL EQUATIONS, pg. 237*XII. AN INVARIANT SURFACE THEOREM FOR A NON-DEGENERATE SYSTEM, pg. 243*XIII. AN APPLICATION OP PERIODIC SURFACES (SOLUTION OF A SMALL DIVISOR PROBLEM), pg. 257*XIV. REPEATING SOLUTIONS FOR A DEGENERATE SYSTEM, pg. 261*XV. BOUNDS FOR PERIODS OF PERIODIC SOLUTIONS, pg. 269*XVI. ONE-DIMENSIONAL REPEATING CURVES IN THE NON-DEGENERATE CASE, pg. 277*Backmatter, pg. 288

Volume

[v. 1] ISBN 9780691079318

Description

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-20), Volume I, will be forthcoming.

Table of Contents

*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. ix*I. ON SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS, pg. 1*II. OSCILLATION OF A THIRD ORDER NONLINEAR AUTONOMOUS SYSTEM, pg. 39*III. NON-LINEAR DELAY DIFFERENTIAL EQUATIONS, pg. 89*IV. FORCED OSCILLATIONS IN NONLINEAR SYSTEMS, pg. 149*V. SINGULAR PERTURBATIONS OF A VAN DER POL EQUATION, pg. 243*VI. THE EXISTENCE OF FORCED PERIODIC SOLUTIONS OF SECOND ORDER DIFFERENTIAL EQUATIONS NEAR CERTAIN EQUILIBRIUM POINTS OF THE UNFORCED EQUATION, pg. 291*VII. ON THE CONSTRUCTION OF PERIODIC SOLUTIONS OF SINGULAR PERTURBATION PROBLEMS, pg. 313

Volume

v. 4 ISBN 9780691079325

Description

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-41), Volume IV, will be forthcoming.

Table of Contents

*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*I. On the Non-Linear Difference-Differential Equation y1(t) = [A - By(t-r) ly (t), pg. 1*II. On the Critical Points of a Class of Differential Equations, pg. 19*III. Optimal Discontinuous Forcing Terms, pg. 29*IV. On the Structure of Symmetric Periodic Solutions of Conservative Systems, with Applications, pg. 53*V. Asymptotic Behavior of Solutions of Canonical Systems Near a Closed, Unstable Orbit, pg. 85*VI. Small Periodic Perturbations of an Autonomous System of Vector Equations, pg. 111*VII. Rotated Vector Fields and an Equation for Relaxation Oscillations, pg. 125*VIII. A Survey of Lyapunov's Second Method, pg. 141*IX. On Phase Portraits of Critical Points in n-Space, pg. 167*X. On Non-Linear Repulsive Forces, pg. 201*Backmatter, pg. 214

Volume

v. 5 ISBN 9780691079332

Description

The description for this book, Contributions to the Theory of Nonlinear Oscillations (AM-45), Volume V, will be forthcoming.

Table of Contents

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

Volume

v. 2 ISBN 9780691095813

Description

These two new collections, numbers 28 and 29 respectively in the Annals of Mathematics Studies, continue the high standard set by the earlier Annals Studies 20 and 24 by bringing together important contributions to the theories of games and of nonlinear differential equations.

Table of Contents

*Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*I. Van der Pol's Equation for Relaxation Oscillations, pg. 1*II. Perturbations of Linear Systems with Constant Coefficients Possessing Periodic Solutions, pg. 19*III. Dynamical Systems with Stable Structures, pg. 37*IV. Notes on Differential Equations, pg. 61*V. A method for the Calculation of Limit Cycles by Successive Approximation, pg. 75*VI. Asymptotic Expansions of Solutions of Systems of Ordinary Linear Differential Equations Containing a Parameter, pg. 81

by "Nielsen BookData"

Details

• NCID: BA02610017
• ISBN:
  • 0691079315
  • 0691095817
  • 0691079110
  • 0691079323
  • 0691079331
• LCCN: 60012225
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Princeton
• Pages/Volumes: 5 v.
• Size: 22-26 cm
• Classification:
  • LCC : QA871
  • DC : 531.3
• Subject Headings:
  • LCSH : Oscillations
• Parent Bibliography ID:
  • BA00300336