scholarly journals Solution about a singular point of a linear differential equation involving a large parameter

1959 ◽  
Vol 91 (3) ◽  
pp. 410-410 ◽  
Author(s):  
Robert McKelvey
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Linear Differential Equation ◽  
Large Parameter ◽  
Linear Differential

scholarly journals On [p,q]-order of growth of solutions of complex linear differential equations near a singular point

Filomat ◽  
2019 ◽  
Vol 33 (13) ◽  
pp. 4013-4020
Author(s):  
Jianren Long ◽  
Sangui Zeng
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Linear Differential Equations ◽  
Order Of Growth ◽  
Complex Linear ◽  
Linear Differential ◽  
Growth Of Solutions

We investigate the [p,q]-order of growth of solutions of the following complex linear differential equation f(k)+Ak-1(z) f(k-1) + ...+ A1(z) f? + A0(z) f = 0, where Aj(z) are analytic in C? - {z0}, z0 ? C. Some estimations of [p,q]-order of growth of solutions of the equation are obtained, which is generalization of previous results from Fettouch-Hamouda.

Stability and Response of Systems Satisfying a Second-Order Linear Differential Equation with Time-Dependent Coefficients

1957 ◽  
Vol 8 (1) ◽  
pp. 78-86
Author(s):  
A. W. Babister
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Linear Differential Equation ◽  
Second Order ◽  
Time Dependent ◽  
Order Linear Differential Equation ◽  
Order Linear ◽  
Oscillatory Nature ◽  
Linear Differential ◽  
Image Position

SummaryThe differential equation considered iswhere all the a’s and b’s are real constants.The nature of the solution is investigated in the neighbourhood of the singular point and the conditions are found for logarithmic terms to be absent.The conditions for stability for large values of τ are determined; the system is stable ifare all positive for large values of τ.The form of the response is considered and its oscillatory (or non-oscillatory) nature investigated. The Sonin-Polya theorem is used to determine simple inequalities which must hold between the coefficients of the differential equation in any interval for the relative maxima of | x | to form an increasing or decreasing sequence in that interval.

scholarly journals Holomorphic solutions about an irregular singular point of an ordinary linear differential equation

1985 ◽  
Vol 39 (2) ◽  
pp. 178-186 ◽  
Author(s):  
C. E. M. Pearce
Keyword(s):  
Differential Equation ◽  
Singular Point ◽  
Linear Differential Equation ◽  
Ordinary Linear Differential Equation ◽  
Holomorphic Solution ◽  
Linearly Independent ◽  
Irregular Singular Point ◽  
Zero Radius ◽  
Linear Differential ◽  
Indicial Equation

AbstractIt is shown that that an ordinary linear differential equation may possess a holomorphic solution in a neighbourhood of an irregular singular point even though the usual linearly independent solutions corresponding to the two roots of the indicial equation both have zero radius of convergence.

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