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

Some 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 ∂ N u ( x , t ) ∂ t N - a ( t ) Δ u + ∑ i = 1 n p i ( x , t ) u ( x , t - σ i ) - ∑ j = 1 m q i ( x , t ) u ( x , t - τ j ) + h ( t ) f ( u ( x , t - r 1 ) , … , u ( x , t - r l ) ) = 0 , ( x , t ) ∈ Ω × [ t 0 , + ∞ ) ≡ G , t 0 ∈ R , where N is an odd integer, Ω is a bounded domain in R M 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).