Oscillation of higher-order neutral partial functional differential equations

Abstract

Some sufficient conditions are established for the oscillation of higher-order neutral partial functional differential equations of the form ∂ n ∂t n [u(x,t)−p(t)u(x,t−τ)]=a(t)Δu(x,t)+ ∑ k=1 s a k(t)Δu(x,t−ρ k(t)) , −q(x,t)u(x,t)− ∑ j=1 m q j(x,t)u(x,t−σ j(t)), (x,t)ϵΩ×[0,∞)G where n ≥ 1 is an odd integer, Ω is a bounded domain in R N with a piecewise smooth boundary δΩ, and Δ is the Laplacian in Euclidean N-space R N .