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A singular perturbation problem

A. G. Ramm
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Abstract

Consider the equation $-s^2Δu_s+q(x)u_s=f(u_s)$ in $\R^3$, $|u(\infty)|<\infty$, $s=const>0$. Under what assumptions on $q(x)$ and $f(u)$ can one prove that the solution $u_s$ exists and $\lim_{s\to 0} u_s=u(x)$, where $u(x)$ solves the limiting problem $q(x)u=f(u)$? These are the questions discussed in the paper.

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A. G. Ramm. 2004-10-20. A singular perturbation problem. https://arxiv.org/abs/math/0410451

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