“SUBMERSIVITY” OF A SOLUTION OF THE EQUATION
z(n)(t)+p₁(t)z^(n-1)(t)+p_n(t) z(t) = αq(t)

Monika Kováčová

   The main goal is to study certain properties of the solution of the differential equation (2) which are very appropriate for exploring the Property A. One can describe these properties verbally as the ability of the function not to overcome a certain level ε for a certain time interval [t > t₀ + δ]. The function having these properties behaves as follows: from a certain t>t₀, it dives under a certain level of ε and keeps being under this level maximally during a time interval δ. For the sake of brevity let us call this behavior of the function “submersivity”. We have found a criterion of “submersivity” as the simplest possible conditions to be imposed on the left side of the equation (2).

Keywords: linear nonhomogeneous equation, estimation of a solution

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