Existence results for a class of variational quasi-mixed hemivariational-like inequalities. (English) Zbl 1491.49008
Summary: The paper aims to explore the existence results for a class of variational quasi-mixed hemivariational-like inequality problems with nonlinear terms in reflexive Banach spaces, which contain variational and hemivariational inequalities. We make use of stable \((\eta,\psi)\)-quasimonotonicity, KKM theorem, Clarke’s generalized directional derivative and Clarke’s generalized gradient to derive the existence theorems for the condition of the constrained set being bounded. Further, we obtain the solution’s existence results when the constrained set is unbounded by utilizing suitable coercive conditions. Moreover, we present some sufficient conditions to assure the boundedness of the solutions set. Besides, we also demonstrate a necessary and sufficient criteria for a restricted class of variational quasi-mixed hemivariational-like inequality problems. Several applications of the main results are illustrated. The new developments improve and generalize some well-known works.
MSC:
| 49J40 | Variational inequalities |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 49J27 | Existence theories for problems in abstract spaces |
Keywords:
variational quasi-mixed hemivariational-like inequality problem; KKM theorem; existence results; stable \((\eta,\psi)\)-quasimonotone; coercivity conditionsReferences:
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