On buckling problems

The buckling problem for a column of unit length and volume leads to the di fferential 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 associa ted functions). These results are established by a self-adjoint approach in the Sobolev space W-2(2)(0, 1) provided the boundary conditions are symmet ric, 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 Dirichl et boundary conditions the eigenfunctions satisfy two additional boundary c onditions of order 3.