Analog of Hayman's Theorem and its Application to Some System of Linear Partial Differential Equations

摘要

We used the analog of known Hayman’s theorem to study the boundednessof L-index in joint variables of entire solutions of some linear higherordersystems of PDE’s and found sufficient conditions providing the boundedness,where L(z) = (l1(z), . . . , ln(z)), lj : Cn → R+ is a continuous functionj ∈ {1, . . . , n}. Growth estimates of these solutions are also obtained.We proposed the examples of systems of PDE’s which prove the exactnessof these estimates for entire solutions. The obtained results are new evenfor the one-dimensional case because of the weakened restrictions imposedon the positive continuous function l.