It is proved: if \(\phi(\tau,\xi)\) is a scalar continuous real function of arguments \(\tau\in [a_{(n-1)},\ b_{(n-1)}]\subset R^{n-1},\) \(\xi \in [a,\ b]\subset R^{1}\) and \(\phi(\tau,a)\phi(\tau,b)<0\) for all \(\tau,\) then for all \(\varepsilon >0\) there exists a continuous function \(\phi_{0}(\tau,\xi)\) such that \(|\phi(\tau,\xi)-\phi_{0}(\tau,\xi)|<\varepsilon,\) and the equation \(\phi_{0}(\tau,\xi)=0\) has a solution continuously dependent on \(\tau\). The assertion is applied to the proof of the solvability of a finite system of nonlinear equations, to the estimation of the number of solutions. We give illustrating examples.

证明：如果\（\ phi（\ tau，\ xi）\）是自变量\（\ tau \ in [a _ {（n-1）}，\ b _ {（n-1）中 ）的标量连续实函数}] \ subset R ^ {n-1}，\）\（\ xi \ in [a，\ b] \ subset R ^ {1} \）和\（\ phi（\ tau，a）\ phi（\ tau蛋白，b）<0 \）对于所有\（\ tau蛋白，\） ，那么对于所有\（\ varepsilon> 0 \）存在一个连续函数\（\ phi_ {0}（\ tau蛋白，\ⅹⅰ）\）这样即\（| \披（\ tau蛋白，\ XI） - \ phi_ {0}（\ tau蛋白，\ⅹⅰ）| <\ varepsilon，\）以及公式\（\ phi_ {0}（\ tau蛋白，\ⅹⅰ） = 0 \）的解决方案连续依赖于\（\ tau \）。该断言可用于证明非线性方程组的可解性，可用于估计解数。我们举例说明。