Perturbation of zero surfaces

It is proved that if a smooth function $u(x)$, $x\in {\mathbb{R}}^3$, such that ${\inf }_{s\in S}\mathrm{\mid }{u}_N(s)\mathrm{\mid }>0$, where $u_N$ is the normal derivative of $u$ on $S$, has a closed smooth surface $S$ of zeros, then the function $u(x)+\epsilon v(x)$hasalsoaclosedsmoothsurface$S_\epsilon$ofzeros\mathrm{.}Here$v$ is a smooth function and $ϵ>0$ is a sufficiently small number.