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The fixed points and iterated order of some differential polynomials

Benharrat Belaidi — 2009

Commentationes Mathematicae Universitatis Carolinae

This paper is devoted to considering the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f ' ' + A 1 ( z ) f ' + A 0 ( z ) f = F , where A 1 ( z ) , A 0 ( z ) ( ¬ 0 ) , F are meromorphic functions of finite iterated p -order.

Some Results on the Properties of Differential Polynomials Generated by Solutionsof Complex Differential Equations

Zinelâabidine LATREUCHBenharrat BELAÏDI — 2015

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

This paper is devoted to considering the complex oscillation of differential polynomials generated by meromorphic solutions of the differential equation f ( k ) + A k - 1 ( z ) f ( k - 1 ) + + A 1 ( z ) f ' + A 0 ( z ) f = 0 , where A i ( z ) ( i = 0 , 1 , , k - 1 ) are meromorphic functions of finite order in the complex plane.

Finite logarithmic order meromorphic solutions of linear difference/differential-difference equations

Abdelkader DahmaniBenharrat Belaidi — 2025

Mathematica Bohemica

Firstly we study the growth of meromorphic solutions of linear difference equation of the form A k ( z ) f ( z + c k ) + + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = F ( z ) , where A k ( z ) , ... , A 0 ( z ) and F ( z ) are meromorphic functions of finite logarithmic order, c i ( i = 1 , ... , k , k ) are distinct nonzero complex constants. Secondly, we deal with the growth of solutions of differential-difference equation of the form i = 0 n j = 0 m A i j ( z ) f ( j ) ( z + c i ) = F ( z ) , where A i j ( z ) ( i = 0 , 1 , ... , n , j = 0 , 1 , ... , m , n , m ) and F ( z ) are meromorphic functions of finite logarithmic order, c i ( i = 0 , ... , n ) are distinct complex constants. We extend some previous results obtained...

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