On the oscillation of first-order differential equations with deviating arguments and oscillatory coefficients

Abstract

In this work, we study the oscillation problem of first-order differential equations with deviating arguments and oscillatory coefficients. We generalize and improve the work of Kwong [30] such that the delay (advanced) and the coefficient functions do not need to be monotone and nonnegative, respectively. This method essentially improves many known oscillation conditions. The significance and the substantial improvement of our results are shown by two illustrative examples.

Keywords

• oscillation
• differential equations
• nonmonotone delays
• oscillatory coefficients