A topological approach to hemivariational inequalities with unilateral growth condition

• Autorzy: Motreanu D. , Naniewicz Z.
• Języki publikacji: EN

Abstrakty

EN

The present paper is devoted to the study of the existence solution problem for a hemivariational inequality on vector-valued function space in the case when the nonlinear nonconvex part satisfies the unilateral growth condition. The critical point theory combined with the Galerkin approximation method have been used to establish the result.

Słowa kluczowe

EN

hemivariational inequality; critical point theory; unilateral growth condition

PL

teoria punktu krytycznego; jednostronny warunek wzrostu

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2001
• Tom: Vol. 7, nr 1
• Strony: 23--41
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Motreanu D.

• Département de Mathématiques, Université de Perpignan 52, Avenue de Villeneuve 66860 Perpignan Cedex, France

autor

Naniewicz Z.

• Cardinal Stefan Wyszyński University, Faculty of Mathematics, Dewajtis 5, 01-815 Warsaw, Poland

Bibliografia

• [1] Ambrosetti, A. and Rabinowitz, P. H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
• [2] Chang, K. C., Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
• [3] Clarke, F. H., Optimization and Nonsmooth Analysis, John Wiley & Sons, New York,
• [4] Dinca, G., Panagiotopoulos, P. D. and Pop, G., Inéqualités hémi-variationnelles semi-coercives sur des ensembles convexes, C. R. Acad. Sei. Paris Sér. I 320 (1995),
• [5] Duvaut, G. and Lions, J.-L., Les Inéquations en Mécanique et en Physique, Travaux et Recherches Mathématiques 21 (1972), Dunod, Paris.
• [6] Ekeland, I. and Temam, R., Convex Analysis and Variational Problems, North- Holland, Amsterdam, 1976.
• [7] Goeleven, D. and Motreanu, D., Eigenvalue and dynamic problems for variational and hemivariational inequalities, Comm. Appl. Nonlinear Anal. 3 (1996), 1-21.
• [8] Haslinger, J., Miettinen, M. and Panagiotopoulos, P. D., Finite Element Method for Hemivariational Inequalities. Theory, Methods and Applications, Kluwer Academic Publishers, Dordrecht, 1999.
• [9] Mistakidis, E. S. and Stavroulakis, G. E., Nonconvex Optimization in Mechanics. Smooth and Nonsmooth Algorithms, Heuristic and Engineering Applications by the F.E.M., Kluwer Academic Publishers, Dordrecht, 1998.
• [10] Motreanu, D., Existence of critical points in a general setting, Set-Valued Anal. 3 (1995) , 295-305.
• [11] Motreanu, D. and Naniewicz, Z., Discontinuous semilinear problems in vector-valued function spaces, Differential Integral Equations 9 (1996), 581-598.
• [12] Motreanu, D. and Panagiotopoulos, P. D., An eigenvalue problem for a hemivariational inequality involving a nonlinear compact operator, Set-Valued Anal. 3 (1995), 157-166.
• [13] Motreanu, D. and Panagiotopoulos, P. D., Nonconvex energy functions, Related, eigenvalue hemivariational inequalities on the sphere and applications, J. Global Op- tim. 6 (1995), 163-177.
• [14] Motreanu, D. and Panagiotopoulos, P. D., On the eigenvalue problem for hemivariational inequalities: existence and multiplicity of solutions, J. Math. Anal. Appl. 197 (1996) , 75-89.
• [15] Motreanu, D. and Panagiotopoulos, P. D., Double eigenvalue problems for hemivariational inequalities, Arch. Rational Mech. Anal. 140 (1997), 225-251.
• [16] Motreanu, D. and Panagiotopoulos, P. D., Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, 1999.
• [17] Naniewicz, Z., Hemi-variational inequalities: Static problems, in “Encyclopedia of Optimization”, Kluwer Academic Publishers, (to appear).
• [18] Naniewicz, Z., Semicoercive variational-hemivariational inequalities with unilateral growth condition, J. Global Optim., (to appear).
• [19] Naniewicz, Z., Hemivariational inequalities with functions fulfilling directional growth condition, Appl. Anal. 55 (1994), 259-285.
• [20] Naniewicz, Z., Hemivariational inequalities as necessary conditions for optimality for a class of nonsmooth nonconvex functionals, Nonlinear World 4 (1997), 117-133.
• [21] Naniewicz, Z. and Panagiotopoulos, P. D., Mathematical Theory of Hemivariational Inequalities and Applications, Marcel Dekker, New York, 1995.
• [22] Panagiotopoulos, P. D., Non-convex superpotentials in the sense of F. H. Clarke and applications, Mech. Res. Comm. 8 (1981), 335-340.
• [23] Panagiotopoulos, P. D., Non-convex energy functionals. Applications to non-convex elastoplasticity, Mech. Res. Comm. 9 (1982), 23-29.
• [24] Panagiotopoulos, P. D., Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions, Birkhäuser Verlag, Basel, Boston, 1985.
• [25] Panagiotopoulos, P. D., Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, New York, 1993.
• [26] Pop, G., Panagiotopoulos, P. D. and Naniewicz, Z., Variational-hemivariational inequalities for multidimensional superpotential laws, Numer. Funct. Anal. Optim. 18 (1997) , 827-856.
• [27] Rabinowitz, H., Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math. 65 (1986), Amer. Math. Soc., Providence, R. I.
• [28] Szulkin, A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 3 (1986), 77-109.