Summary
A method is constructed which yields a strip containing the full solution sets of nonlinear eigenvalue problems of the formu=λTu.
The strip can be narrowed iteratively, and the method applies for both stable and unstable branches. Its high degree of accuracy is demonstrated by numerical examples. In particular, a lower bound is given for the critical value at which criticality is lost in the thermal ignition problem for the unit ball.
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Sprekels, J. Exact bounds for the solution branches of nonlinear eigenvalue problems. Numer. Math. 34, 29–40 (1980). https://doi.org/10.1007/BF01463996
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DOI: https://doi.org/10.1007/BF01463996