ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary Eigenvalue problems, arising from questions of stability or in connection with vibrations, may be approached (a) as problems of the calculus of variations, (b) by establishing their differential equation, (c) by means of their integral (or integrodifferential) equation. Up to the present, method (b) has been farther developped than the other ones; still it does not apply to problems whose eigenvalue figures explicitly in the boundary conditions. In order to overcome this defect, it is advisable to use method (a) which, from a physical point of view, offers the advantage of facilitating the mathematical interpretation of mechanical restrictions and vice versa. The authors intend (i) to generalize the theory of eigenvalues for the above mentioned case and (ii) to establish the connections between methods (a), (b), and (c) on a most general scale, viz. for so called “natural problems”. In this first communication, they connect methods (a) and (b), restricting themselves to the case of one independant and one dependant variable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02009323
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