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Online ISSN 1552-4485; Print ISSN 0033-569X
On oscillation of nonlinear delay differential equations
Authors:
M. R. S. Kulenović, G. Ladas and A. Meimaridou
Journal:
Quart. Appl. Math. 45 (1987), 155-164
MSC:
Primary 34K15
DOI:
https://doi.org/10.1090/qam/885177
MathSciNet review:
885177
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Necessary, sufficient, and necessary and sufficient conditions are obtained for all solutions of the nonlinear differential equation \[ \frac {{dy}}{{dt}} + \sum \limits _{j = 1}^n {{q_j}f\left ( {y\left ( {t - {\tau _j}} \right )} \right ) = 0,\qquad t \ge 0,} \qquad \left ( * \right )\] to be oscillatory. These conditions are expressed in terms of the characteristic equation of the corresponding linear “variational” equation \[ \frac {{dy}}{{dt}} + \sum \limits _{j = 1}^n {{q_j}y\left ( {t - {\tau _j}} \right ) = 0, \qquad t \ge 0. \qquad \left ( { * * } \right )} \] Our results show that for a certain class of nonlinear functions $f,\left ( * \right )$ oscillates if and only if $\left ( { * * } \right )$ oscillates. As an application of our results, we obtain simple sufficient and necessary and sufficient conditions for the oscillation of several nonlinear delay differential equations which appear in applications.
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© Copyright 1987
American Mathematical Society