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Hemivariational inequalities with a general growth condition: existence and approximation. (English) Zbl 1033.49011

The authors establish both an existence and an approximation result for a general class of hemivariational inequalities that contain a potential with a superquadratic growth. First, by applying refined methods in the nonsmooth critical point theory in the sense of Clarke, the authors obtain the existence of nontrivial solutions. Next, a convergence result for Galerkin type approximation is established in the paper. One of the main novelties of this work is that Assumption (H4) improves the celebrated growth condition of A. Ambrosetti and P. H. Rabinowitz [J. Funct. Anal. 14, 349-381 (1973; Zbl 0273.49063)]. The approach allows the authors to cover in a unifying way the superlinear and sublinear situations. Significant classes of problems described by the abstract results are also illustrated in the present paper.

MSC:

49J40 Variational inequalities
47J20 Variational and other types of inequalities involving nonlinear operators (general)
47J30 Variational methods involving nonlinear operators
49J52 Nonsmooth analysis

Citations:

Zbl 0273.49063
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