Oscillation and asymptotic behavior for a class of delay parabolic differential

Some comparative theorems are given for the oscillation and asymptotic behavior for a class of high order delay parabolic differential equations of the form ∂n(u(x,t)−p(t)u(x,t−τ))∂tn−a(t)△u+c(x,t,u)+∫abq(x,t,ξ)f(u(x,g1(t,ξ)),…,u(x,gl(t,ξ)))dσ(ξ)=0,(x,t)∈Ω×R+≡G, where nn is an odd integer, ΩΩ is a bounded domain in RmRm with a smooth boundary ∂Ω∂Ω, and △△ is the Laplacian operation with three boundary value conditions. Our results extend some of those of [P. Wang, Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments, Appl. Math. Comput. 106 (1999), 163–169] substantially.