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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).

MSC:

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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