Sharp oscillation theorem for fourth-order linear delay differential equations

Abstract

Abstract In this paper, we present a single-condition sharp criterion for the oscillation of the fourth-order linear delay differential equation x ( 4 ) ( t ) + p ( t ) x ( τ ( t ) ) = 0 $$ x^{(4)}(t) + p(t)x\bigl(\tau (t)\bigr) = 0 $$ by employing a novel method of iteratively improved monotonicity properties of nonoscillatory solutions. The result obtained improves a large number of existing ones in the literature.

Keywords

• Fourth-order differential equation
• Delayed argument
• Oscillation
• Sharp criterion