Unbounded perturbations of forced harmonic oscillations at resonance

Author:
Tung Ren Ding

Journal:
Proc. Amer. Math. Soc. **88** (1983), 59-66

MSC:
Primary 34C25; Secondary 34E10, 58F30, 70K40

MathSciNet review:
691279

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Abstract | References | Similar Articles | Additional Information

Abstract: In 1969, A. C. Lazer and D. E. Leach proved an existence theorem for periodic solutions of Duffing's equations with bounded perturbations at resonance. In the present note, with the use of a topological technique, the author extended some results of Lazer and Leach to an -dimensional Duffing system with unbounded perturbations at resonance.

**[1]**A. C. Lazer,*On Schauder’s fixed point theorem and forced second-order nonlinear oscillations*, J. Math. Anal. Appl.**21**(1968), 421–425. MR**0221026****[2]**Jean Mawhin,*An extension of a theorem of A. C. Lazer on forced nonlinear oscillations*, J. Math. Anal. Appl.**40**(1972), 20–29. MR**0313587****[3]**A. C. Lazer and D. E. Leach,*Bounded perturbations of forced harmonic oscillators at resonance*, Ann. Mat. Pura Appl. (4)**82**(1969), 49–68. MR**0249731****[4]**L. Césari,*Nonlinear problems across a point of resonance for non-self-adjoint systems*, Nonlinear Analysis (A Collection of Papers in Honor of Erich H. Rothe, edited by L. Césari, et al.), Academic Press, New York, 1978.**[5]**Tong Ren Ding,*Nonlinear oscillations at a point of resonance*, Sci. Sinica Ser. A**25**(1982), no. 9, 918–931. MR**681856****[6]**-,*Some fixed point theorems and periodically perturbed non-dissipative system*, Ann. of Math. (2)**2**(1981), 281-297.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1983-0691279-X

Keywords:
Duffing's equations,
high dimension,
resonance,
unbounded perturbations,
periodic solutions,
existence theorem,
topological technique

Article copyright:
© Copyright 1983
American Mathematical Society