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Properties of entire solutions of some linear PDE's

Bandura A, Skaskiv O., Filevych P.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

17--28

In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.