Displaying similar documents to “On the hyper order of solutions of a class of higher order linear differential equations.”

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

Abdallah El Farissi, Benharrat Belaidi (2012)

Applications of Mathematics

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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 , ⋯ , k - 1 ) , D j ( z ) ( j = 0 , 1 ) , F ( z ) are entire functions with max { ρ ( A j ) ( j = 0 , 1 , ⋯ , k - 1 ) , ρ ( D j ) ( j = 0 , 1 ) } < 1 . We also investigate the relationship between small functions and the solutions of the above equation.