Oscillation for a class of odd-order delay parabolic differential equations

AbstractSome sufficient conditions and some sufficient and necessary conditions are established for the oscillation of a class of odd-order delay parabolic differential equations of the form ∂Nu(x,t)∂tN-a(t)Δu+∑i=1npi(x,t)u(x,t-σi)-∑j=1mqi(x,t)u(x,t-τj)+h(t)f(u(x,t-r1),…,u(x,t-rl))=0,(x,t)∈Ω×[t0,+∞)≡G,t0∈R,where N is an odd integer, Ω is a bounded domain in RM with a smooth boundary ∂Ω, and Δ is the Laplacian operation with three different boundary conditions. To some extent, our results extended and improved the oscillatory results of some references. Meanwhile, we corrected some mistakes in a main conclusion of reference (J. Comput. Appl. Math. 147 (2002) 263)