Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition

• Autorzy: Naniewicz Z.
• Języki publikacji: EN

Abstrakty

EN

A variational-hemivariational inequality on a vector valued function space is studied with the nonlinear part satisfying the unilateral growth condition. The higher order term is assumed to be pseudo-monotone and semicoercive. The compatibility condition expressed in terms of a recession functional has been proposed and the existence result has been formulated in a form involving the notion of discontinuous subgradient.

Słowa kluczowe

EN

variational-hemivariational inequality; unilateral growth condition; discontinuous subgradient

PL

nierówność wariacyjno-hemiwariacyjna; jednostronne warunki wzrostu

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 2
• Strony: 223--244
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Naniewicz Z.

• Cardinal Stefan Wyszynski University Faculty of Mathematics and Science, Dewajtis 5, 01-815 Warsaw, Poland,

Bibliografia

• BAIOCCHI, C., BUTTAZZO, G ., GASTALDI, F. and TOMARELLI, F. (1988) General existence theorems for unilateral problems in continuum mechanics'. Arch. Rational Mech. Anal. 100, 149- 188.
• BREZIS, H. (1968) Equations et inequations non-lineaires dans les espaces vectoriels en dualite. Comm. Pure Appl. Math. 18, 115- 176. B
• REZIS, H. and NIRENBERG, L. ( 1978) Characterizations of the ranges of some nonlinear operators and applications to boundary value problems. Ann. Scuola Normale Superiore Pisa, Classe di Scienze V , 225- 326.
• BROWDER, F.E. and HESS, P. (1972) Nonlinear mappings of monotone type in Banach spaces. J. Funct. Anal. 11, 251- 294.
• CLARKE, F.H. (1983) Optimization and Nonsmooth Analysis. John Wiley & Sons.
• DUVAUT, G. and LIONS, J.L. (1972) Les Inequations en Mecanique et en Physique. Dunod.
• EKELAND, I. and TEMAM, R. (1976) Convex Analysis and Variational Problems. North-Holland.
• GOELEVEN, D. (1996) Noncoercive Variational Problems and Related Topics. Vol. 357 of Pitman Research Notes in Mathematics Series, Longman.
• GOELEVEN, D. and THERA, M. (1995) Semicoercive variational hemivariational inequalities. J. Global Optim. 6, 367-381.
• HEDBERG, L.I. (1978) Two approximation problems in function spaces. Ark. Mat. 16, 51- 81.
• KUFNER, A., JOHN, 0. and FUCIK, S. (1977) Function Spaces. Academia.
• MoTREANU, D. and NANIEWICZ, Z. (1996) Discontinuous semilinear problems in vector-valued function spaces. Differential and Integral Equations 9, 581- 598.
• MOTREANU, D. and NANIEWICZ, Z. (2001) A topological approach to hemivariational inequalities with unilateral growth condition. J. Appl. Anal. 7, 23- 41.
• MOTREANU, D. and NANIEWICZ, Z. (2002) Semilinear hemivariational inequalities with Dirichlet boundary condition. In: Y. Gao, D. and R. W. Ogden, eds. Advances in Mechanics and Mathematics: AMMA 2002. Advances in Mechanics and Mathematics, Kluwer Academic Publishers, 89-110.
• MOTREANU, D. and PANAGIOTOPOULOS, P. D. (1995) Nonconvex energy functions, Related eigenvalue hemivariational inequalities on the sphere and applications. J. Global Optimiz. 6, 163-177.
• MOTREANU, D. and PANAGIOTOPOULOS, P. D. (1996) On the eigenvalue problem for hemivariational inequalities: existence and multiplicity of solutions. J. Math. Anal. Appl. 197, 75- 89.
• MOTREANU, D. and PANAGIOTOPOULOS, P .D. (1999) Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities. Kluwer Academic Publishers.
• NANIEWICZ, Z. (1994a) Hemivariational inequalities with functions fulfilling directional growth condition. Appl. Anal. 55, 259- 285.
• NANIEWICZ, Z. (1994b) Hemivariational inequality approach to constrained problems for star-shaped admissible sets. J. Optim. Theory Appl. 83, 97- 112.
• NANIEWICZ, Z. (1995a) Hemivariational inequalities with functionals which are not locally Lipschitz. Nonlinear Anal. 25, 1307-1320.
• NANIEWICZ, Z. (1995b) On variational aspects of some nonconvex nonsmooth global optimization problem. J. Global Optim. 6, 383- 400.
• NANIEWICZ, Z. (1997) Hemivariational inequalities as necessary conditions for optimality for a class of nonsmooth nonconvex functionals. Nonlinear World4 , 117- 133.
• NANIEWICZ, Z. (2000) Semicoercive variational-hemivariational inequalities with unilateral growth condition. J. Global Optim. 17, 317-337.
• NANIEWICZ, Z. and PANAGIOTOPOULOS, P.D. (1995) Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker.
• PALLASCHKE, D. and ROLEWICZ, 8. (1997) Foundation of Mathematical Optimization. Kluwer Academic Publishers.
• PANAGIOTOPOULOS, P.D. (1981) Non-convex superpotentials in the sense of F.H. Clarke and applications. Mech. Res. Comm. 8, 335- 340.
• PANAGIOTOPOULOS, P. D. (1983) Noncoercive energy function, hemivariational inequalities and substationarity principles. Acta Mech. 48, 160- 183.
• PANAGIOTOPOULOS, P.D. (1985) Inequality Problems in Mechanics and Applications. Convex and Nonconvex Energy Functions. Birkhiiuser Verlag.
• PANAGIOTOPOULOS, P.D. (1993) Hemivariational Inequalities. Applications in Mechanics and Engineering. Springer-Verlag.
• POP, G., PANAGIOTOPOULOS, P.D. and NANIEWICZ, Z. (1997) Variationalhemivariational inequalities for multidimensional superpotential laws. Numer. Funct. Anal. Optim. 18, 827- 856.