Oscillation of solutions for certain impulsive vector parabolic differential equations with delays ✩

In this paper, sufficient conditions are established for H-oscillation of solutions of the following impulsive vector parabolic differential equations with delays ⎧⎪ ⎪⎪⎪⎪⎪⎪⎪⎨⎪ ⎪⎪⎪⎪⎪⎪⎪⎩ ∂ ∂t U(x, t) = a(t) U(x, t) + m k=1 bk(t) U(x, t − τk) − l h=1 qh(x, t)U(x, t −σh) +F(x, t), t = tj , U x, t+j −U x, t−j = p(x, tj )U(x, tj ), j ∈ I∞, (x,t) ∈ Ω ×R+ ≡ G, where R+ = [0,∞), Ω is a bounded domain in Rn with a piecewise smooth boundary ∂Ω, and H is a unit vector in RM. © 2006 Elsevier Inc. All rights reserved