Oscillation of delay parabolic differential equations with several coefficients

Abstract

Some new sufficient conditions are established for the oscillation of delay parabolic differential equations of the form (E) ∂u(x,t) ∂t =a(t) Δu− ∑ i=1 n p i(x,t)u(x,t−σ i)+ ∑ j=1 m q j(x,t)u(x,t−τ j), (x,t)∈Ω×[t 0,∞)≡G where Ω is a bounded domain in R n with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space R n with three different boundary conditions. Our results improve the well-known oscillation result of (E) when n= m=1. An example is considered to illustrate our main results.