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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Application of a lemma on bilinear forms to a problem in nonlinear oscillations


Author: A. C. Lazer
Journal: Proc. Amer. Math. Soc. 33 (1972), 89-94
MSC: Primary 34C15
MathSciNet review: 0293179
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Abstract: In this note we give a simple condition for nondegeneracy of symmetric bilinear forms on infinite dimensional vector spaces. We apply this condition and elementary properties of Fourier series to prove a uniqueness theorem for periodic solutions of a class of second order nonlinear differential systems.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0293179-9
PII: S 0002-9939(1972)0293179-9
Keywords: Newtonian equations of motion, Sylvester's law of inertia, Parseval's formula
Article copyright: © Copyright 1972 American Mathematical Society