Oscillations of solutions of vector differential equations of parabolic type with functional arguments

Vector parabolic differential equations with functional arguments are studied and the oscillations of solutions of boundary value problems are investigated. Our approach is to reduce the oscillation problems to the nonexistence of positive solutions of scalar differential inequalities by employing the concept of H-oscillation introduced by Domšlak (see: R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, New York, 1996), where H denotes a unit vector.