Abstract
We consider the convergence of solution curves of approximations to parameter-dependent operator equations of the form G(λ, x) = 0. Provided Gx(λ, x) remains non-singular this problem is catered for by a simple extension to standard theory. In this paper, however, attention is concentrated on solution curves through certain singular points (λ0, x0), and the main result is that convergence depends on consistency and stability results for the linear eigenvalue problem Gx(λ0, x0)0 = 0.
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