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Transactions of the American Mathematical Society

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Oscillation, continuation, and uniqueness of solutions of retarded differential equations


Authors: T. Burton and R. Grimmer
Journal: Trans. Amer. Math. Soc. 179 (1973), 193-209
MSC: Primary 34K15
DOI: https://doi.org/10.1090/S0002-9947-1973-0324171-9
Erratum: Trans. Amer. Math. Soc. 187 (1974), 429.
MathSciNet review: 0324171
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Abstract: In this paper we present a number of results on continuation and uniqueńess of solutions of the n-dimensional system $ x'(t) = f(t,x(t)) + g(t,x(t - \tau (t)))$ for $ \tau (t) \geq 0$. We then give some necessary, some sufficient, and some necessary and sufficient conditions for oscillation of solutions of the second order equation $ x'' + a(t)f(x(t - \tau (t))) = 0$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0324171-9
Keywords: Oscillation, continuation, uniqueness
Article copyright: © Copyright 1973 American Mathematical Society

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