ar X iv : m at h - ph / 0 40 50 01 v 1 3 M ay 2 00 4 A nonlinear singular perturbation problem
نویسنده
چکیده
Let F (u ε) + ε(u ε − w) = 0 (1) where F is a nonlinear operator in a Hilbert space H, w ∈ H is an element, and ε > 0 is a parameter. Assume that F (y) = 0, and F ′ (y) is not a boundedly invertible operator. Sufficient conditions are given for the existence of the solution to (1.1) and for the convergence lim ε→0 u ε − y = 0. An example of applications is considered. In this example F is a nonlinear integral operator.
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