scholarly journals Growth and Bounded Solution of Second-Order of Complex Differential Equations Through of Coefficient Function

2020 ◽  
Vol 871 ◽  
pp. 012057
Author(s):  
Haneen Abbas Saleh ◽  
Shatha S. Alhily
Keyword(s):  
Differential Equations ◽  
Bounded Solution ◽  
Second Order ◽  
Coefficient Function ◽  
Complex Differential Equations

scholarly journals Algebroid Solutions of Second Order Complex Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Lingyun Gao ◽  
Yue Wang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Maximum Modulus ◽  
Second Order ◽  
Algebraic Differential Equation ◽  
Order Complex ◽  
Maximum Modulus Principle ◽  
Value Distribution Theory ◽  
Order Algebraic ◽  
Complex Differential Equations

Using value distribution theory and maximum modulus principle, the problem of the algebroid solutions of second order algebraic differential equation is investigated. Examples show that our results are sharp.

scholarly journals On the Growth of Solutions of Second Order Linear Complex Differential Equations whose Coefficients Satisfy Certain Conditions

2020 ◽  
Vol 17 (2) ◽  
pp. 0530
Author(s):  
Ayad Alkhalidy ◽  
Eman Hussein
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Infinite Order ◽  
Second Order ◽  
The Other ◽  
Nontrivial Solutions ◽  
Linear Complex ◽  
Order Linear ◽  
Complex Differential Equations ◽  
Growth Of Solutions

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

Oscillatory criteria for the second order linear ordinary differential equations

2019 ◽  
Vol 69 (4) ◽  
pp. 857-870
Author(s):  
Gevorg A. Grigorian
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riccati Equation ◽  
Second Order ◽  
Equation Method ◽  
Coefficient Function ◽  
Order Linear ◽  
Linear Ordinary Differential Equations ◽  
Mathieu’S Equation ◽  
Function Potential

Abstract The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations. We show that the first of these criteria in the continuous case of the coefficient function (potential) of the equation implies the J. Deng’s oscillatory criterion. An extremal oscillatory condition for the Mathieu’s equation is obtained. The obtained results are compared with some known oscillatory criteria.

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