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 .

On One Class of Algebraic Differential Equations

Vestnik MEI ◽  
2021 ◽  
pp. 135-137
Author(s):  
Irina N. Dorofeeva ◽  
◽  
Viktoriya A. Podkopaeva ◽  
Aleksandr Ya. Yanchenko ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Part ◽  
Rational Functions ◽  
Second Order ◽  
Algebraic Differential Equations ◽  
All Solutions ◽  
Order Algebraic ◽  
Integer Solutions ◽  
Linear Differential

The article addresses second-order algebraic differential equations that have a separated linear part and admit a finite-order integer function as a solution. All possible integer solutions of such equations are described. It is shown that all solutions are the solutions of certain second-order linear differential equations the coefficients of which are represented by rational functions. It has been demonstrated that any such integer function y = f(z) is either a solution of the algebraic equation R(z, exp{Q(z)}, y) ≡ 0 (where R is a polynomial of three variables, and Q(z) is a polynomial of one variable), or a solution of a differential equation with separable variables y′ = a(z)y (for some rational function a(z)).

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

scholarly journals On the Existence of Eigenmodes of Linear Quasi-Periodic Differential Equations and their Relation to the MHD Continuum

1982 ◽  
Vol 37 (8) ◽  
pp. 830-839 ◽  
Author(s):  
A. Salat
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Infinite Sequence ◽  
Periodic Coefficient ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Magnetic Surfaces ◽  
Toroidal Geometry

The existence of quasi-periodic eigensolutions of a linear second order ordinary differential equation with quasi-periodic coefficient f{ω1t, ω2t) is investigated numerically and graphically. For sufficiently incommensurate frequencies ω1, ω2, a doubly indexed infinite sequence of eigenvalues and eigenmodes is obtained.The equation considered is a model for the magneto-hydrodynamic “continuum” in general toroidal geometry. The result suggests that continuum modes exist at least on sufficiently ir-rational magnetic surfaces

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