Oscillation of solutions of systems of neutral type partial functional differential equations

Abstract

Sufficient conditions are established for the oscillation of solutions of systems of neutral type partial functional differential equations of the form ∂/∂t (p(t) ∂/∂t (ui(x, t) + ∑r=1 d λr(t)ui(x, t - τr(t)))) = ai(t)Δui(x, t) + ∑j=1 m∑k=1 s aijk(t)Δuj (x, ρk(t)) - qi(x, t)ui(x, t) - ∑j=1 m∑h=1 l qijh(x, t)uj(x, σh(t)), (x, t) ∈ Ω × [0, ∞) ≡ G, i = 1, 2, ..., m, where Ω is a bounced domain in ℝn with a piecewise smooth boundary ∂Ω, and Δ is the Laplacian in Euclidean n-space ℝn. The obtained results are illustrated by some interesting examples.