Abstract
For regular coercive inhomogeneous and eigenvalue problems of the form b(u,γ) −zk(u,γ)=(f,γ), γεH, with bounded bilinearforms b, k in a Hilbertspace H the approximate solutions, eigenfunctions and eigenvalues calculated by means of the Galerkin method are shown to converge, with the eigenvalues preserving algebraic multiplicity. The above class of regular coercive problems are applicable to integral and differential equations and include for example the K-p.d. and non-K-p.d. operators of PETRYSHYN as special cases.
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Grigorieff, R.D. Über die Lösung regulärer koerzitiver Rand- und Eigenwertaufgaben mit dem Galerkinverfahren. Manuscripta Math 1, 385–411 (1969). https://doi.org/10.1007/BF01172144
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DOI: https://doi.org/10.1007/BF01172144