Abstract
The buckling problem for a column of unit length and volume leads to the differential equation -(py ")" = lambda y " on a finite interval with various sets of boundary conditions. In, this paper completeness, minimality, and basis theorems are proved for the corresponding eigenfunctions (and associated functions). These results are established by a self-adjoint approach in the Sobolev space ...
Abstract
The buckling problem for a column of unit length and volume leads to the differential equation -(py ")" = lambda y " on a finite interval with various sets of boundary conditions. In, this paper completeness, minimality, and basis theorems are proved for the corresponding eigenfunctions (and associated functions). These results are established by a self-adjoint approach in the Sobolev space W-2(2)(0, 1) provided the boundary conditions are symmetric, and by a more general non-self-adjoint approach in me spaces W-2(k)(0, 1), k = 0, 1,..., 4. A new observation is that e.g. in the case of Dirichlet boundary conditions the eigenfunctions satisfy two additional boundary conditions of order 3.
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