On forced oscillation of higher order functional differential equations

Abstract In this paper, we establish some new oscillation criteria for the following forced functional differential equation x ( n ) ( t ) + q ( t ) | x ( τ ( t ) ) | λ - 1 x ( τ ( t ) ) = e ( t ) , t ∈ [ t 0 , ∞ ) . No restriction is imposed on the forcing term e ( t ) to be the n th derivative of an oscillatory function. Two cases have been taken into consideration: (i) q ( t ) 0 , λ > 1 and τ ( t ) ⩽ t ( ⩾ t ) ; (ii) q ( t ) changes its sign, 0  λ τ ( t ) ⩽ t ( ⩾ t ) . The main results generalize some existing results and can be applied to the oscillation problem that are not covered in the literature.

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