ABSTRACT
Recently the fundamental theory for partial differential equations with deviations has undergone an intensive development. However, the qualitative theory of these important classes for applications of partial differential equations is still in an initial stage of its development. Especially, only a few results have been published so far which deal with the oscillatory properties of the solutions of parabolic differential equations with deviating arguments. We refer the reader to the papers by Bykov and Kulatev [1], Kreith and Ladas [4], Yoshida [7], [8], Mishev and Bainov [5], and Cui [2]. But the necessary and sufficient condition for oscillation of solutions of parabolic equations has not been studied.
