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Boundary value problems and Green’s operator functions. (English) Zbl 0712.34024

Using specific methods from algebraic analysis, the author establishes some existence and uniqueness results for a boundary value problem corresponding to a second order differential operator; this framework is specific to the linear theory of small oscillations of a continuum.
The particularity of the employed methods rests upon the fact that the results are obtained without increasing the dimension of the problem. For the finite dimensional case a closed form of the problem is obtained.
Reviewer: G.Sebe

MSC:

34B05 Linear boundary value problems for ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34G10 Linear differential equations in abstract spaces
47A60 Functional calculus for linear operators
47A62 Equations involving linear operators, with operator unknowns
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