In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing \(\lim \sup\) and \(\lim \inf\) on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
We study the oscillation of first-order delay equations using a method that parallels the use of Riccati equations in the study of the oscillation of second-order ordinary differential equations without delay. We give an alternative proof of a comparison theorem first established by Kwong and Patula, obtain some asymptotic behaviors of nonoscillatory solutions, prove a new criterion that falls within a gap left open by established results, and confirm a conjecture raised by Hunt and Yorke.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.