A Schrödinger singular perturbation problem

Details A Schrödinger singular perturbation problem A Schrödinger singular perturbation problem

2005-11-14

arxiv.org/abs/math-ph/0511049v1

Physics

Mathematical Physics

Scientific paper

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

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