On the number of L2-solutions of second order linear differential equations

1978 ◽  
Vol 80 (1-2) ◽  
pp. 1-13 ◽  
Author(s):  
Ian Knowles
Keyword(s):  
Differential Equations ◽  
Vector Space ◽  
Function Space ◽  
Second Order ◽  
Linear Differential Equations ◽  
Order Linear ◽  
All Solutions ◽  
Linear Differential

SynopsisLet d denote the dimension of the vector space consisting of all solutions of the equation − (p(t)y′)′ + q(t)y = 0, a ≤ t < ∞; that lie in the function space L2[a, ∞). By means of certain bounds on the solutions of this equation, sufficiency criteria are obtained for the cases d = 0 and d = 2.

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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