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Zbl 0848.49013
Goeleven, D.; Mentagui, D.
Well-posed hemivariational inequalities.
(English)
[J] Numer. Funct. Anal. Optimization 16, No.7-8, 909-921 (1995). ISSN 0163-0563; ISSN 1532-2467/e

Let $V$ be a real reflexive Banach space with topological dual $V^*$. Let $K$ be a closed convex subjset of $V$ and $f\in V^*$. In this paper, the authors have obtained some basic results concerning the well-posedness for hemivariational inequalities of finding $u\in K$ such that $$\langle Au+ Tu- \rho, \nu- u\rangle+ \int_\Omega j^0 (x, u(x); \nu(x)- u(\alpha)) d\Omega \geq 0, \qquad \text {for all } \nu\in K,$$ where $j^0 (x,u(x); \nu(x)- u(x))$ denotes the generalized directional derivative of the function $j(x)$ at $u(x)$ in the direction $\nu (x)- u(x)$ and $T,A: V\to V^*$ are nonlinear operators.
MSC 2000:
*49J40 Variational methods including variational inequalities
90C33 Complementarity problems

Keywords: existence results; well-posedness; hemivariational inequalities; generalized directional derivative

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