Copyright © 2010 Quanwen Lin and Rongkun Zhuang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present some new oscillation criteria for second-order neutral partial functional differential equations of the form (∂/∂t){p(t)(∂/∂t)[u(x,t)+∑i=1lλi(t)u(x,t-τi)]}=a(t)Δu(x,t)+∑k=1sak(t)Δu(x,t-ρk(t))-q(x,t)f(u(x,t))-∑j=1mqj(x,t)fj(u(x,t-σj)), (x,t)∈Ω×R+≡G, where Ω is a bounded domain in the Euclidean N-space RN with a piecewise smooth boundary ∂Ω and Δ is the Laplacian in RN. Our results improve some known results and show that the oscillation of some second-order linear ordinary differential equations implies the oscillation of relevant nonlinear neutral partial functional differential equations.