Forced oscillation of a class of neutral hyperbolic differential equations

In this paper, we study the following boundary value problem for a class of neutral hyperbolic differential equations: ∂ 2 ∂ t 2 [ u + c ( t ) u ( x , t - τ ) ] = a 0 ( t ) Δ u + a 1 ( t ) Δ u ( x , t - ρ ) - ∫ a b q ( x , t , ξ ) f ( u [ x , g ( t , ξ ) ] ) d μ ( ξ ) + g ( x , t ) , ( x , t ) ∈ Ω × R + ≡ G , ∂ u ∂ N + ν ( x , t ) u = 0 , ( x , t ) ∈ ∂ Ω × R + . A number of theorems for oscillatory solutions of the problem under two different cases are developed.