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Hemivariational inequalities governed by the p-Laplacian - Neumann problem

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.
Rocznik
Strony
727--754
Opis fizyczny
Bibliogr. 37 poz.
Twórcy
autor
  • Cardinal Stefan Wyszyński University Department of Mathematics and Natural Sciences, College of Science, Dewajtis 5, 01-815 Warsaw, Poland, naniewicz@uksw.edu.pl
Bibliografia
  • ANANE, A. and GOSSEZ, J. P. (1990) Strongly nonlinear elliptic problems near resonance: a variational approach. Comm. Partial Diff. Eqns 15, 1141-1159.
  • ARCOYA, D. and ORSINA, L. (1997) Landesman-Lazer conditions and quasi-linear elliptic equations. Nonlinear Anal. 28, 1623-1632.
  • 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.
  • BOUCHALA, J. and DRABEK, P. (2000) Strong resonance for some quasilinear elliptic equations. J. Math. Anal. Appl. 245, 7-19.
  • BROWDER, F.E. and HESS, P. (1972) Nonlinear mappings of monotone type in Banach spaces. J. Fund. Anal 11, 251-294.
  • CHANG, K.C. (1981) Variational methods for non-differentiable functional and their applications to partial differential equations. J. Math. Anal. Appl. 80, 102-129.
  • CLARKE, F.H. (1983) Optimization and Nonsmooth Analysis. John Wiley & Sons, New York.
  • DUVAUT, G. and LIONS, J.L. (1972) Les Inéquations en Mécanique et en Physique. Dunod, Paris.
  • EKELAND, I. and TEMAM, R. (1976) Convex Analysis and Variational Problems. North-Holland, Amsterdam - New York.
  • GASIŃSKI, L. and PAPAGEORGIOU, N.S. (2001a) An existence theorem for nonlinear hemivariational inequalities at resonance. Bull. Austr. Math. Soc. 63, 1-14.
  • GASIŃSKI, L. and PAPAGEORGIOU, N.S. (2001b) Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance. Proc. Royal Soc. Edinburgh 131A, 1091-1111.
  • GASIŃSKI, L. and PAPAGEORGIOU, N.S. (2005) Nonsmooth Critical Point Theory and Nonlinear Boundary Value Problems. Chapman & Hall, CRC Press, Boca Raton.
  • GOELEVEN, D., MOTREANU, D. and PANAGIOTOPOULOS, P.D. (1997) Multiple solutions for a class of eigenvalue problems in hemivariational inequalities. Nonlinear Anal. 29, 9-26.
  • GOELEVEN, D. and THERA, M. (1995) Semicoercive variational hemivariational inequalities. J. Global Optim. 6, 367-381.
  • HALIDIAS, N. and NANIEWICZ, Z. (2004) On a class of hemivariational inequalities at resonance. J. Math. Anal. Appl. 289, 584-607.
  • HEDBERG, L.I. (1978) Two approximation problems in function spaces. Ark. Mat. 16, 1-81.
  • 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 NANIEWICZ, Z. (2003) A minimax approach to semicoercive hemivariational inequalities. Optimization 52, 541-554.
  • 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. (1994) Hemivariational inequalities with functions fulfilling directional growth condition. Applicable Analysis 55, 259-285.
  • NANIEWICZ, Z. (1995) Hemivariational inequalities with functional which are not locally Lipschitz. Nonlinear Anal. 25, 1307-1320.
  • NANIEWICZ, Z. (1997) Hemivariational inequalities as necessary conditions for optimality for a class of nonsmooth nonconvex functional. Nonlinear World 4, 117-133.
  • NANIEWICZ, Z. (2003) Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition. Control & Cybernetics 32, 223-244.
  • NANIEWICZ, Z. (2004) Hemivariational inequalities governed by the p-Laplacian - Dirichlet problem. Control & Cybernetics 33, 181-210.
  • NANIEWICZ, Z. and PANAGIOTOPOULOS, P.D. (1995) Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York.
  • PALLASCHKE, D. and ROLEWICZ, S. (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. Birkhäuser Verlag.
  • PANAGIOTOPOULOS, P.D. (1993) Hemivariational Inequalities. Applications in Mechanics and Engineering. Springer-Verlag.
  • PAPAGEORGIOU, N.S. and PAPALINI, F. (2000) Existence and multiplicity results for nonlinear eigenvalue problems with discontinuities. Ann. Polon. Math. LXXV, 125-141.
  • PAPALINI, F. (2002) Nonlinear Eigenvalue Neumann Problems with Discontinuities. J. Math. Anal. Appl. 273, 137-152.
  • RADULESCU, V. (1993) Mountain pass theorems for nondifferentiable functions and applications. Proc. Japan. Acad. Sci., Ser. A, Math. Sci. 69, 193-198.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0017-0065
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