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

 

A comparison theorem for certain functional differential equations


Author: Ernest D. True
Journal: Proc. Amer. Math. Soc. 47 (1975), 127-132
MathSciNet review: 0352657
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Abstract | References | Additional Information

Abstract: The oscillatory character of solutions to the functional differential equation $ {x^{(n)}}(t) + a(t)f(x(g(t))) = Q(t)$ is investigated, by comparison with the oscillatory character of solutions to $ {x^{(n)}}(t) + s(t)f(x(t)) = 0$ where $ s(t) \geqslant \gamma a(t),0 < \gamma < 1$. Here, $ Q(t)$ represents a bounded, oscillatory forcing function, and $ g(t)$ tends to $ \infty $ as $ t \to \infty $ or $ g(t) \geqslant t - c$ for large $ t$ but is otherwise arbitrary.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0352657-7
PII: S 0002-9939(1975)0352657-7
Keywords: Functional differential equation, oscillation, comparison, forcing function
Article copyright: © Copyright 1975 American Mathematical Society