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Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem

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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 (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).
Rocznik
Strony
181--210
Opis fizyczny
Bibliogr. 36 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. (1988) Etude des valeurs propres et de la ŕesonance pour 1’oṕerateur p-Laplacien. PhD thesis, Universite Libre de Bruxelles, Brussels.
  • Anane, A. and Gossez, J.P. (1990) Strongly nonlinear elliptic problems nearresonance: 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 typein Banach spaces. J. Funct. Anal. 11, 251-294.
  • Chang, K.C. (1981) Variational methods for non-differentiable functionals 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.
  • Duvaut, G .and Lions, J.L. (1972) Les Ińequations en Ḿecanique et en Physique. Dunod.
  • Ekeland, I. and Temam, R. (1976) Convex Analysis and Variational Problems. North-Holland.
  • Fleckinger-Pelĺe, J. and Tḱăc, P. (2002) An improved Poinca ́e inequality and the p-Laplacian at resonance. Advances in Differential Equations 7, 951-971.
  • Gasiński, L. and Papageorgiou, N. S. (2001a) An existence theorem fornonlinear hemi-variational inequalities at resonance. Bull. Austr. Math. Soc. 63, 1-14.
  • Gasiński, L. and Papageorgiou, N.S. (2001b) Multiple solutions for semi-linear hemivariational inequalities at resonance. Publ. Math. Debrecen 51,1-26.
  • Gasiński, L. and Papageorgiou, N.S. (2001c) Solutions and multiple solutions for quasilinear hemivariational inequalities at resonance. Proc. Royal Soc. Edinburgh 131A, 1091-1111.
  • 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 Th́era, 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, 51-81.
  • Lindgvist, P. (1990) On the equationdiv(|Dx|p−2Dx) +λ|x|p−2x= 0.Pro-ceedings of the American Math. Society 109 (1).
  • 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. Advancesin 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 andapplications. 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. (1997) Hemivariational inequalities as necessary conditions foroptimality for a class of nonsmooth nonconvex functionals. Nonlinear World 4, 117-133.
  • Naniewicz, Z. (2003) Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition. Control and Cybernetics 32, 223-244.
  • Naniewicz, Z. and Panagiotopoulos, P. D. (1995)Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker.
  • 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. Birkhauser Verlag.
  • Panagiotopoulos, P. D. (1993) Hemivariational Inequalities. Applicationsin Mechanics and Engineering. Springer-Verlag.
  • Papalini, F. (2002) Nonlinear Eigenvalue Neumann Problems with Discontinuities. J. Math. Anal. Appl. 273, 137-152.
  • Radulescu, V. (1993) Mountain pass theorems for nondifferentiable functionsand applications. Proc. Japan. Acad. Sci., Ser. A, Math. Sci. 69, 193-198.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0007-0050
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