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On Buckling Problems
Author(s) -
Tretter C.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200009)80:9<633::aid-zamm633>3.0.co;2-1
Subject(s) - mathematics , eigenfunction , boundary value problem , sobolev space , mathematical analysis , dirichlet boundary condition , interval (graph theory) , dirichlet distribution , boundary (topology) , space (punctuation) , pure mathematics , eigenvalues and eigenvectors , combinatorics , physics , quantum mechanics , linguistics , philosophy
The buckling problem for a column of unit length and volume leads to the differential equation —( py ″)″ = λ 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 the 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.