A complete analysis of a model nonlinear singular perturbation problem having a continuous locus of singular points
نویسندگان
چکیده
منابع مشابه
A nonlinear singular perturbation problem
Let F (uε) + ε(uε − 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) and for the convergence limε→0 ‖uε−y‖ = 0. An example of applications is considered. In this example F is a nonlinear ...
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15 صفحه اول00 4 A singular perturbation problem
Consider the equation −ε 2 ∆u ε + q(x)u ε = f (u ε) in R 3 , |u(∞)| < ∞, ε = const > 0. Under what assumptions on q(x) and f (u) can one prove that the solution u ε exists and lim ε→0 u ε = u(x), where u(x) solves the limiting problem q(x)u = f (u)? These are the questions discussed in the paper.
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 1981
ISSN: 0196-8858
DOI: 10.1016/0196-8858(81)90004-x