Oscillations in differential equations caused by non-monotone arguments

Abstract

This paper is concerned with the oscillatory behavior of first-order linear differential equations with variable non-monotone deviating arguments and nonnegative coefficients. Corresponding differential equations of both delay and advanced type are studied. Sufficient oscillation conditions involving $% \lim \sup $ and $\lim \inf $ are obtained by applying an iterated method. An example, numerically solved in MATLAB, is also given to illustrate the applicability and strength of the obtained conditions over known ones.