A Two-Sided Functional-Discrete Method for Second-Order Differential Equations with General Boundary Conditions

2004 ◽  
Vol 40 (7) ◽  
pp. 1029-1042
Author(s):  
I. I. Lazurchak ◽  
V. L. Makarov
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Second Order ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Discrete Method ◽  
Second Order Differential Equations

Boundary value problems for systems of second order differential equations

1985 ◽  
Vol 101 (1-2) ◽  
pp. 61-76 ◽  
Author(s):  
L. H. Erbe ◽  
H. W. Knobloch
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of A Solution ◽  
Differential Systems ◽  
Second Order Differential Equations

SynopsisWe consider boundary value problems for second order differential systems of the form (1)x” = A(t)x′ + f(t, x) and (2) x” = A(t)x′ + f(t, x) + q(t, x). By assuming the existence of a solution to (1) with a given region in (t, x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of and satisfies given boundary conditions.

scholarly journals Closed-Form Solutions of Linear Ordinary Differential Equations with General Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 226
Author(s):  
Efthimios Providas ◽  
Stefanos Zaoutsos ◽  
Ioannis Faraslis
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Closed Form ◽  
Linear Operators ◽  
General Boundary ◽  
Order Differential Operator ◽  
General Boundary Conditions ◽  
Symbolic Form ◽  
Closed Form Solutions

This paper deals with the solution of boundary value problems for ordinary differential equations with general boundary conditions. We obtain closed-form solutions in a symbolic form of problems with the general n-th order differential operator, as well as the composition of linear operators. The method is based on the theory of the extensions of linear operators in Banach spaces.

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