Summary
In this report it is proved that the method ofGalerkin remains valid for a certain class of linear, non-self-adjoint eigenvalue problems. This class contains all eigenvalue problems which arise from originally self-adjoint problems by addition of a linear differential expression which destroys the former self-adjointness.Helge von Koch's theory of infinite determinants is used in deriving the above result.
This is a preview of subscription content, log in via an institution to check access.
Literatur
S. G. Michlin,Variationsmethoden der mathematischen Physik, Akademie-Verlag, Berlin 1962, S. 356–389.
V. V. Bolotin,Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, Oxford-London-New York-Paris 1963, S. 257–265.
H. Leipholz,Über die Konvergenz des Galerkinschen Verfahrens bei nichtselbstadjungierten und nichtkonservativen Eigenwertproblemen, ZAMP14, 70–79 (1963).
G. Hamel,Integralgeichungen, Springer-Verlag, Berlin-Göttingen-Heidelberg 1949, S. 130, 131.
H. Leipholz,Über die Konvergenz des Verfahrens von Galerkin bei quasi-linearen Randwertproblemen, Acta Mechanica1, 250–261 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leipholz, H. Über die Zulässigkeit des Verfahrens von Galerkin bei linearen, nichtselbstadjungierten Eigenwertproblemen. Journal of Applied Mathematics and Physics (ZAMP) 16, 837–843 (1965). https://doi.org/10.1007/BF01614114
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01614114