Summary
We state three theorems concerning iterative methods for solving equations containing monotone, but not necessarily uniformly monotone operators in Hilbert space, which may be not Lipschitz bounded, thus extending results obtained by Sibony [9, 10]. We apply the method to a nonlinear elliptic Dirichlet problem of laminar flow theory of non Newtonian fluids, thus improving the rather experimental treatment given in Ames [1] and removing the condition of nonzero difference quotients assumed by Cryer [3].
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Literatur
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Sachs, A. Iterationsverfahren für monotone, nicht notwendig Lipschitz-beschränkte Operatoren im Hilbert-Raum. Numer. Math. 20, 356–363 (1972). https://doi.org/10.1007/BF01402558
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DOI: https://doi.org/10.1007/BF01402558