DOI: 10.24193/fpt-ro.2023.2.17

Authors: Mircea Sofonea and Andaluzia Matei

Abstract: We consider a mixed hemivariational-variational problem, i.e., a system which gathers a hemivariational inequality with a constrained variational inequality. We list the assumptions on the data and prove the existence of a unique solution to the problem. Subsequently, we prove the continuous dependence of the solution with respect to the data. Then, we deduce a criterion of convergence to the solution of the mixed hemivariational-variational inequality, i.e., we formulate necessary and sufficient conditions which guarantee the convergence of a sequence to the unique solution of the system. The proof of our results is based on the particular structure of the problem which allows us to employ a fixed point argument. Finally, we provide two examples which illustrate our abstract results.

Key Words and Phrases: Mixed hemivariational-variational problem, fixed point, unique solvability, convergence results.

2010 Mathematics Subject Classification: 47J20, 49J40, 47J30, 47H10, 74B99.

Published on-line: June 15th, 2023.

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