## 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.