scholarly journals Properties of solutions of an infinite system of ordinary linear differential equations of the first order with auxiliary boundary conditions

1930 ◽  
Vol 32 (2) ◽  
pp. 284-284 ◽  
Author(s):  
William T. Reid
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Infinite System ◽  
Linear Differential Equations ◽  
First Order ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

Gewöhnliche lineare Differentialgleichungen n−ter Ordnung mit Distributionskoeffizienten

1980 ◽  
Vol 85 (3-4) ◽  
pp. 291-298 ◽  
Author(s):  
Rainer Pfaff
Keyword(s):  
Differential Equations ◽  
Continuous Solution ◽  
Initial Conditions ◽  
Linear Differential Equations ◽  
First Order ◽  
Integrable Functions ◽  
Leibniz Formula ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations ◽  
Derivatives Of

SynopsisWe give a formula (4) for a variety of ordinary linear differential equations of order n with distributional coefficients. There appear as coefficients distributions of order k ≦ n/2, i.e. these distributions are kth distributional derivatives of locally L-integrable functions. With a suitable transformation (7) the differential equations can be transformed into first order systems (8) with integrable coefficients. From this follows the existence of a continuous solution, which can be uniquely determined by proper initial conditions.The coefficients in the differential equations considered are chosen as general as possible but such that a transformation into a system with integrable coefficients can be performed, and that all products are defined by Leibniz' formula.

scholarly journals On the Composition of Simultaneous Differential Systems of the First Order

1932 ◽  
Vol 3 (2) ◽  
pp. 128-131
Author(s):  
M. Mursi-Ahmed
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Differential Equations ◽  
Differential Systems ◽  
Order Linear ◽  
First Order ◽  
Linear Differential ◽  
Image Position

§ 1. Consider the system of n first order linear differential equations:together with the n boundary conditionswhere aij, bij are constants and where we assume for simplicity of notation that gii = 0.

scholarly journals Limit Behavior of Solutions of Ordinary Linear Differential Equations

1994 ◽  
Vol 1 (3) ◽  
pp. 315-323
Author(s):  
František Neuman
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Linear Differential Equations ◽  
Limit Behavior ◽  
Limit Sets ◽  
Equivalent Linear ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

Abstract A classification of classes of equivalent linear differential equations with respect to ω-limit sets of their canonical representatives is introduced. Some consequences of this classification to the oscillatory behavior of solution spaces are presented.

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.

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