Sensitivity analysis for strongly nonlinear quasi-variational inclusions. (English) Zbl 0960.47035

It is proved that the solutions of the problem \(0\in N(u,u,\lambda)+M(u,u,\lambda)\) in a Hilbert space depend continuously on the parameter \(\lambda\). Here, \(M(\cdot,u,\lambda)\) is maximal monotone and such that the corresponding resolvent operator \((I+\rho M(\cdot,u,\lambda))^{-1}\) satisfies a Lipschitz condition with respect to \(u\), \(N(\cdot,u,\lambda)\) is strongly monotone and Lipschitz, and \(N(u,\cdot,\lambda)\) is Lipschitz (always with appropriate constants).


47J20 Variational and other types of inequalities involving nonlinear operators (general)
65K10 Numerical optimization and variational techniques
47H05 Monotone operators and generalizations
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