Goeleven, D.; Mentagui, D. Well-posed hemivariational inequalities. (English) Zbl 0848.49013 Numer. Funct. Anal. Optimization 16, No. 7-8, 909-921 (1995). Let \(V\) be a real reflexive Banach space with topological dual \(V^*\). Let \(K\) be a closed convex subjset of \(V\) and \(f\in V^*\). In this paper, the authors have obtained some basic results concerning the well-posedness for hemivariational inequalities of finding \(u\in K\) such that \[ \langle Au+ Tu- \rho, \nu- u\rangle+ \int_\Omega j^0 (x, u(x); \nu(x)- u(\alpha)) d\Omega \geq 0, \qquad \text{for all } \nu\in K, \] where \(j^0 (x,u(x); \nu(x)- u(x))\) denotes the generalized directional derivative of the function \(j(x)\) at \(u(x)\) in the direction \(\nu (x)- u(x)\) and \(T,A: V\to V^*\) are nonlinear operators. Reviewer: M.A.Noor (Riyadh) Cited in 29 Documents MSC: 49J40 Variational inequalities 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) Keywords:existence results; well-posedness; hemivariational inequalities; generalized directional derivative PDF BibTeX XML Cite \textit{D. Goeleven} and \textit{D. Mentagui}, Numer. Funct. Anal. Optim. 16, No. 7--8, 909--921 (1995; Zbl 0848.49013) Full Text: DOI References: [1] Adams R. A., Sobolev spaces (1975) [2] Attouch H., Variational convergence for functions and operators (1984) · Zbl 0561.49012 [3] Banatiotopoulos C. C., ZAMM 69 pp 489– (1989) [4] Clarke F. H., Nonsmooth analysis and optimization (1984) · Zbl 0727.90045 [5] Dontchev A. L., lectures notes in mathematics (1543) [6] Goeleven D., FUNDP Research-Report (1994) [7] Karamanlis H. N., Journal Mech. (1994) [8] DOI: 10.1080/01630568108816100 · Zbl 0479.49025 [9] DOI: 10.1080/01630568308816145 · Zbl 0517.49007 [10] Mosco U., lecture notes in mathematics 543 pp 83-156– (1976) [11] Naniewicz Z., Journal of Optimization Theory and Applications 543 (1976) [12] Naniewicz, Z. and Panagiotopoulos, P. D. 1995. ”Mathematical theory of hemivariational inequalities and applications”. New York: Dekker. · Zbl 0968.49008 [13] DOI: 10.1016/0362-546X(91)90224-O · Zbl 0733.49012 [14] Panagiotopoulos P. D., C.R. Acad. Sci. Paris, t. 307 pp 735– (1988) [15] DOI: 10.1007/BF00041685 · Zbl 0712.73059 [16] Panagiotopoulos P. D., Quaterly of Applied Mathematics 3 pp 409– (1988) · Zbl 0672.73011 [17] Panagiotopoulos P. D., Quaterly of Applied Mathematics pp 611– (1989) · Zbl 0693.73007 [18] DOI: 10.1002/zamm.19850650608 [19] Panagiotopoulos P. D., Topics in Nonsmooth Mechanics (1988) · Zbl 0646.00014 [20] DOI: 10.1016/0093-6413(81)90064-1 · Zbl 0497.73020 [21] DOI: 10.1007/BF01170410 · Zbl 0538.73018 [22] Panagiotopoulos P. D., Hemivariational inequalities, applications in mechanics and engineering (1993) · Zbl 0826.73002 [23] Pascali D., Nonlinear mappings of monotone type (1978) · Zbl 0423.47021 [24] Revalski, J. 1985. Variational inequalities with unique solution. Mathematics and Education in Mathematics. 14th Spring Conference of the Union of Bulgarian Mathematicians Sofia. 1985. pp.534–541. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.