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Well-posed hemivariational inequalities. (English) Zbl 0848.49013

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.
Reviewer: M.A.Noor (Riyadh)

MSC:

49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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