We treat an example of a nonlinear eigenvalue problem in 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.
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Charles A. Stuart, Gregory Vuillaume, A Discretised Nonlinear Eigenvalue Problem with Many Spurious Branches of Solutions. Z. Anal. Anwend. 20 (2001), no. 1, pp. 183–192DOI 10.4171/ZAA/1009