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Zeitschrift für Analysis und ihre Anwendungen


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Volume 20, Issue 1, 2001, pp. 183–192
DOI: 10.4171/ZAA/1009

Published online: 2001-03-31

A Discretised Nonlinear Eigenvalue Problem with Many Spurious Branches of Solutions

Charles A. Stuart[1] and Gregory Vuillaume[2]

(1) Ecole Polytechnique Federale, Lausanne, Switzerland
(2) Ecole Polytechnique Federale, Lausanne, Switzerland

We treat an example of a nonlinear eigenvalue problem in $L^2(0,1)$ which can be solved explicitly. It has a single branch of non-trivial solutions. Discretisation reduces the problem to a finite-dimensional one having many branches of non-trivial solutions. We investigate the convergence of these approximate solutions.

Keywords: Stokes equations, layer-like domains, Fredholm property, weighted spaces

Stuart Charles, Vuillaume Gregory: A Discretised Nonlinear Eigenvalue Problem with Many Spurious Branches of Solutions. Z. Anal. Anwend. 20 (2001), 183-192. doi: 10.4171/ZAA/1009