Oscillation of delay parabolic differential equations with several coefficients

摘要

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=1npi(x,t)u(x,t−σi)+∑j=1mqj(x,t)u(x,t−τj),(x,t)∈Ω×[t0,∞)≡G where Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space Rn 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.