A minimax approach to the eigenvalue problem of hemivariational inequalities and applications. (English) Zbl 0829.49005

The aim of the present paper is the study of the eigenvalue problem for hemivariational inequalities. The minimax approach applied (Mountain-Pass Theorem) is a generalization, proved in this paper, of a result of Rabinowitz for nonsmooth functionals. The main result of the paper states the existence of a nontrivial solution for the eigenvalue problem. Applications concerning yet unsolved mechanical problems illustrate the theory.


49J40 Variational inequalities
49K35 Optimality conditions for minimax problems
49J52 Nonsmooth analysis
49R50 Variational methods for eigenvalues of operators (MSC2000)
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[1] Panagiotopoulos P. D., CBMS–NSF Regional Conference Series in Applied Mathematics (1985)
[2] DOI: 10.1016/0362-546X(91)90224-O · Zbl 0733.49012
[3] Panagiotopoulos P. D., Hemivariational inequalities. Application to Mechanics and Engineering (1993) · Zbl 0826.73002
[4] Clarke F. H., Optimization and Nonsmooth Analysis (1983) · Zbl 0582.49001
[5] Karamanlis H. N., Buckling problems in composite von Kdrman Plates (1991)
[6] Karamanlis H. N., Journal of the Mech. Behaviour of Materials (Freund Publ., Tel Aviv) 5 pp 25– (1993)
[7] Rabinowitz P. H., CBMS Regional Conf. Sec. in Math. Amer. Math. Soc., Providence, R. I. 65 (1986)
[8] DOI: 10.1016/0022-247X(81)90095-0 · Zbl 0487.49027
[9] DOI: 10.1016/0022-247X(86)90252-0 · Zbl 0599.49008
[10] Montreanu D., Pitman Res. (1993)
[11] DOI: 10.1016/0362-546X(89)90037-0 · Zbl 0696.49018
[12] DOI: 10.1080/00036819208840138 · Zbl 0724.49011
[13] Naniewicz, Z. and Panagiotopoulos, P. D. 1983. ”Mathematical Theory of Hemivariational Inequalities”. N.York: book in press. · Zbl 0968.49008
[14] Aubin J. P., Applied Functional Analysis (1979) · Zbl 0424.46001
[15] DOI: 10.1002/zamm.19850650116
[16] DOI: 10.1002/zamm.19900700103 · Zbl 0723.73026
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