Condition \((S)_+^1\), Altman's condition and the scalar asymptotic derivative: Applications to complementarity theory (Q2702959)

The author studies complementarity problems considered in elasticity of the following form:NEWLINENEWLINENEWLINEfind \(x_0\in K\) such that \(T_0(x_0)\in K^*\) and \(\langle x_0,T_0(x_0) \rangle=0\)NEWLINENEWLINENEWLINEwhere \(K\subset E\) (reflexive Banach space) is a closed cone with the dual \(K^*\) and the operator \(T_0\in E\to E\) has the form \(T_0=I- \lambda\cdot L+T\) where \(I\) is the identity operator. For this problem, the author gives existence results.