Oscillation for a class of neutral parabolic differential equations
Some sufficient conditions are established for the oscillation of a class of neutral parabolic differential equations of the form, partial derivative N(u(x, t) - Sigma(k=1)(r) lambda(k)u (x, t - rho(k)))/partial derivative t(N) -a(t)Delta + Sigma(i=1)(n) p(i) (x, t) u(x, t - sigma(i)) - Sigma(j=1)(m) q(j) (x, t) u (x, t - tau(j)) +h(t) f(u(x, t - r1), ..., u(x, t - r(1))) = 0, (x, t) is an element of Omega x [t0, + infinity) equivalent to G, t(0) is an element of R+, where N is an odd number, Omega is a bounded domain in R-M with a smooth boundary partial derivative Omega, and Delta is the Laplacian operation with three different boundary conditions. We obtained some new oscillatory conditions for the odd-order neutral parabolic differential equation. To some extent, our results are new oscillatory conditions, and extended some oscillatory results of some references. (c) 2005 Elsevier Ltd. All rights reserved.
oscillation neutral parabolic differential equation eventually positive solution