International Journal of Differential Equations
Volume 2010 (2010), Article ID 619142, 12 pages
Research Article

Oscillation for Certain Nonlinear Neutral Partial Differential Equations

1Department of Mathematics, Maoming University, Maoming 525000, China
2Department of Mathematics, Huizhou University, Huizhou 516015, China

Received 29 April 2010; Accepted 16 August 2010

Academic Editor: Qingkai Kong

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.


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.