Necessary and sufficient conditions for oscillation of neutral delay parabolic differential equations

摘要

Necessary and sufficient conditions are established for the oscillation of neutral delay parabolic differential equations of the form∂∂t[u(x,t)−pu(x,t−τ)]=a(t)Δu(x,t)+∑k=1sak(t)Δu(x,t−ρk(t))−∑j=1mqj(t)u(x,t−σj(t)),(x,t)∈Ω×[0,∞)≡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.