On Delay-Independent Criteria for Oscillation of Higher-Order Functional Differential Equations

We investigate the oscillation of the following higher-order functional differential equation: ð ‘¥ ( ð ‘› ) ( ð ‘¡ ) + ð ‘ž ( ð ‘¡ ) | ð ‘¥ ( ð ‘¡ − ð œ ) | 𠜆 − 1 ð ‘¥ ( ð ‘¡ − ð œ ) = ð ‘’ ( ð ‘¡ ) , where ð ‘ž ( ð ‘¡ ) and ð ‘’ ( ð ‘¡ ) are continuous functions on [ ð ‘¡ 0 , ∞ ) , 1 > 𠜆 > 0 and ð œ â‰ 0 are constants. Unlike most of delay-dependent oscillation results in the literature, two delay-independent oscillation criteria for the equation are established in both the case ð œ > 0 and the case ð œ < 0 under the assumption that the potentials ð ‘ž ( ð ‘¡ ) and ð ‘’ ( ð ‘¡ ) change signs on [ ð ‘¡ 0 , ∞ ) .