Displaying similar documents to “Oscillation of solutions of some 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.