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Algebraic methods for solving boundary value problems. (English) Zbl 0652.34020

Summary: By means of the reduction of boundary value problems to algebraic ones, conditions for the existence of solutions and explicit expressions of them are obtained. These boundary value problems are related to the second order operator differential equation \(X^{(2)}+A_ 1X^{(1)}+A_ 0X=0\), and \(X^{(1)}=A+BX+XC\). For the finite- dimensional case, computable expressions of the solutions are given.

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34B99 Boundary value problems for ordinary differential equations
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