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Higher-order linear differential equations with solutions having a prescribed sequence of zeros and lying in the Dirichlet space

Li-Peng Xiao (2015)

Annales Polonici Mathematici

The aim of this paper is to consider the following three problems:i (1) for a given uniformly q-separated sequence satisfying certain conditions, find a coefficient function A(z) analytic in the unit disc such that f”’ + A(z)f = 0 possesses a solution having zeros precisely at the points of this sequence; (2) find necessary and sufficient conditions for the differential equation f ( k ) + A k - 1 f ( k - 1 ) + + A f ' + A f = 0 (*) in the unit disc to be Blaschke-oscillatory; (3) find sufficient conditions on the analytic coefficients of the...

On the growth of solutions of some higher order linear differential equations

Abdallah El Farissi, Benharrat Belaidi (2012)

Applications of Mathematics

In this paper we discuss the growth of solutions of the higher order nonhomogeneous linear differential equation f ( k ) + A k - 1 f ( k - 1 ) + + A 2 f ' ' + ( D 1 ( z ) + A 1 ( z ) e a z ) f ' + ( D 0 ( z ) + A 0 ( z ) e b z ) f = F ( k 2 ) , where a , b are complex constants that satisfy a b ( a - b ) 0 and A j ( z ) ( j = 0 , 1 ...

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