Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations


Author: R. Grimmer
Journal: Trans. Amer. Math. Soc. 198 (1974), 215-228
MSC: Primary 34K15; Secondary 34C10
DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0
MathSciNet review: 0348227
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A number of results are presented on oscillation and growth of nonoscillatory solutions of the differential equation $ {x^{(n)}}(t) + f(t,x(t)) = 0$. It is shown that a nonoscillatory solution satisfies a first-order integral inequality while its $ (n - 1)$st derivative satisfies a first-order differential inequality. By applying the comparison principle, results are obtained by analyzing the two associated first-order scalar differential equations. In the last section it is shown that these results can be easily extended to delay-differential equations.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34K15, 34C10

Retrieve articles in all journals with MSC: 34K15, 34C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0
Keywords: Oscillation, growth, comparison method
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society