Existence and stability for a class of variational–hemivariational inequalities involving multivalued Brezis pseudomonotone operators

Shengda Zeng (), Xi Chen (), Jinxia Cen () and Patrick Winkert ()
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Shengda Zeng: Chongqing Normal University
Xi Chen: Guizhou University
Jinxia Cen: Zhejiang Normal University
Patrick Winkert: Institut für Mathematik

Journal of Global Optimization, 2025, vol. 92, issue 4, No 8, 1043 pages

Abstract: Abstract In this paper, we provide existence and stability results for a new multivalued variational-hemivariational inequality (MVHVI, for short) involving Brezis pseudomonotone operators in a reflexive Banach space. First, we use the Moreau-Yosida approximation to introduce an approximated problem corresponding to (MVHVI), and apply an existence result for nonlinear equilibrium problems, convergence techniques as well as Sion’s Minimax Theorem to prove the existence of solutions of (MVHVI). Then, a stability result for (MVHVI) is obtained via employing Tikhonov regularization and perturbed approach. The theoretical results established in this paper extend the ones in (J Glob Optim 52:743–756, 2012) and (J Glob Optim 56:605–622, 2013). Finally, we study a stationary Navier–Stokes equation with nonmonotone and multivalued constitutive laws for illustrating the validity of the main theoretical results in this paper.

Keywords: Brezis pseudomonotone operator; Existence; Moreau–Yosida approximation; Sion’s minimax theorem; Stability; Tikhonov regularization; Variational–hemivariational inequalities; 35J87; 58E35; 70K20; 26E25; 65J20 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01487-4

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