Oscillation for Certain Nonlinear Neutral Partial Differential Equations

Abstract EN

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.