In this paper we study existence of solutions to the generalized equation 0 ∈ f(p,x) + F(x), where f is a function, F is a set-valued mapping, and p is a parameter. Conditions are given, in terms of metric regularity of F, local convex-valuedness of F^− 1, and partial calmness of f with respect to x uniformly in p, for the property that, for any p near the reference value, the generalized equation has a solution at a certain distance from the reference solution. Some corollaries and applications of this result are also presented.

中文翻译：

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参数化广义方程解的存在性

在本文中，我们研究以解决方案存在的广义方程0∈ ˚F（p，X）+ ˚F（X），其中˚F是一个函数，˚F是一组值映射，和p是参数。条件中给出，在度量正则性方面˚F，局部凸valuedness ˚F ^{- 1}，和的局部平静˚F相对于X均匀地在p中，属性，对于任何p在参考值附近，广义方程的解离参考解有一定距离。还介绍了该结果的一些推论和应用。