On oscillation of delay differential equations with a variable sign potential

Abstract This paper examines the oscillation properties of delay differential equations of the second-order, focusing particularly on systems where the coefficient associated with the non-delayed term exhibits variable sign behavior. Our method allows us to simultaneously analyze both canonical and non-canonical delay differential equations. The study distinguishes between equations with delay and without delay terms and demonstrates the influence of delay on the behavior of solutions. A possible extension to nonlinear equations is also discussed under certain monotonicity constraints.