OSCILLATION CRITERIA FOR SECOND ORDER NEUTRAL PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS

. Some new oscillation criteria are established for second order neutral partial functional differential equation of the form ∂ ∂t " r(t) ∂ ∂t u(x, t) +X l i=1 λi(t)u(x, t − τi) !#= a(t)△u(x, t) +Xs k=1 ak(t)△u(x, t − ρk(t)) − q(x, t)u(x, t) − Xm j=1 qj (x, t)fj (u(x, t − σj )), (x, t) ∈ Ω × [0, ∞) ≡ G under the conditions R∞ t0 r −1 (s)ds = ∞ and R∞ t0 r −1 (s)ds < ∞, respectively. where Ω is a bounded domain in RN with a piecewise smooth boundary ∂Ω and △ is the laplacian in the Euclidean N−space RN .