## Lipschitzian stability of constraint systems and generalized equations.(English)Zbl 0805.93044

A class of multifunctions $$\phi$$ from $$\mathbb{R}^ n$$ into $$\mathbb{R}^ m$$ given in the form $\phi(x):= \{y\in \mathbb{R}^ m: F(x,y)\in \Lambda,\;(x,y)\in \Omega\},\tag{1}$ where $$\Lambda\subset \mathbb{R}^ q$$ and $$\Omega\subset \mathbb{R}^{n+m}$$ are closed sets and $$F: \mathbb{R}^ n\times \mathbb{R}^ m\to \mathbb{R}^ q$$ is a continuous vector function, is considered.
The goal is to establish refined sufficient conditions, on the initial data $$F$$, $$\Lambda$$ and $$\Omega$$ ensuring the pseudo-Lipschitzian property of the multifunction (1).
The paper contains several necessary and sufficient conditions for such a multifunction being pseudo-Lipschitzian. It is also presented background material in nonsmooth analysis connected with nonconvex constructions of the normal cone for sets, the coderivative for multifunctions and the first- and the second-order subdifferentials for extended real-valued functions.

### MSC:

 93D09 Robust stability 34A60 Ordinary differential inclusions

### Keywords:

multifunctions; nonsmooth analysis; coderivative
Full Text:

### References:

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