A singular perturbation problem

Details A singular perturbation problem A singular perturbation problem

2004-10-20

arxiv.org/abs/math/0410451v1

Mathematics

Analysis of PDEs

Scientific paper

Consider the equation $-s^2\Delta u_s+q(x)u_s=f(u_s)$ 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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