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Nonsmooth/Nonconvex Mechanics pp 333–348Cite as

Hemivariational Inequalities Associated to Multivalued Problems with Strong Resonance

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 50))

Abstract

We apply the theory of hemivariational inequalities to obtain several existence results for a multivalued boundary value problem at resonance on an arbitrary open set in ℝN.

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References

  • Ambrosetti, A., and Rabinowitz, P.H. (1973). Dual variational methods in critical point theory and applications, Journal of Functional Analysis 14: 349–381.

    Article  MathSciNet  MATH  Google Scholar 

  • Arcoya, D., and Canada, A. (1990). Critical point theorems and applications to nonlinear boundary value problems, Nonlinear Analysis, Theory, Methods and Applications 14: 393–411.

    Article  MathSciNet  MATH  Google Scholar 

  • Aubin, J.P., and Clarke, F.H. (1979). Shadow prices and duality for a class of optimal control problems, SIAM Journal of Control and Optimization 17: 567–586.

    Article  MathSciNet  MATH  Google Scholar 

  • Chang, K.C. (1981). Variational methods for non-differentiable functionals and their applications to partial differential equations, Journal of Mathematical Analysis and Applications 80: 102–129.

    Article  MathSciNet  MATH  Google Scholar 

  • Clarke, F.H. (1975). Generalized gradients and applications, Transactions of the American Mathematical Society 205: 247–262.

    Article  MathSciNet  MATH  Google Scholar 

  • Clarke, F.H. (1981). Generalized gradients of Lipschitz functionals, Advances in Mathematics 40: 52–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Clarke, F.H. (1983). Optimization and nonsmooth analysis, Willey, New York.

    MATH  Google Scholar 

  • Costa, D.G., and Silva, E.A. (1991). The Palais-Smale condition versus coercivity, Nonlinear Analysis, Nonlinear Analysis, Theory, Methods and Applications 16: 371–381.

    Article  MathSciNet  MATH  Google Scholar 

  • Fichera, G. (1964). Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Mem. Accad. Naz. Lincei 7: 91–140.

    MathSciNet  Google Scholar 

  • Gazzola, F., and Rădulescu, V. (2000). A nonsmooth critical point theory approach to some nonlinear elliptic problems in IRN, Differential and Integral Equations 13: 47–60.

    MathSciNet  MATH  Google Scholar 

  • Landesman, E.A., and Lazer, A.C. (1976). Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech.19: 609–623.

    MathSciNet  Google Scholar 

  • Lions, J.L., and Stampacchia, G. (1967). Variational inequalities, Communications in Pure and Applied Mathematics 20: 493–519.

    Article  MathSciNet  MATH  Google Scholar 

  • Minakshisundaran, S., and Pleijel, A. (1949). Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Canadian Journal of Mathematics 1: 242–256.

    Article  Google Scholar 

  • Moreau, J.J. (1968). La notion de sur-potentiel et ses liaisons unilatérales en élastostatique, C.R. Acad. Sci. Paris, Série I, Mathématiques 267: 954–957.

    MathSciNet  MATH  Google Scholar 

  • Motreanu, D., and Panagiotopoulos, P.D. (1998). Minimax theorems and qualitative properties of the solutions of hemivariational inequalities, Kluwer Academic Publishers, Dordrecht, Boston, London.

    Google Scholar 

  • Naniewicz, Z. and Panagiotopoulos, P.D. (1995). Mathematical theory of hemivariational inequalities and applications, Marcel Dekker, New York.

    Google Scholar 

  • Panagiotopoulos, P.D. (1983). Une généralisation non-convexe de la notion de sur-potentiel et ses applications, C.R. Acad. Sci. Paris, Série II, Mécanique 296: 1105–1108.

    MathSciNet  MATH  Google Scholar 

  • Panagiotopoulos, P.D. (1983). Nonconvex energy functions. Hemivariational inequalities and substationarity principles, Acta Mechanica 42: 160–183.

    MathSciNet  Google Scholar 

  • Panagiotopoulos, P.D. (1988). Nonconvex superpotentials and hemivariational inequalities; Quasidiferentiability in Mechanics, in Nonsmooth Mechanics and Applications, J.J. Moreau and P.D. Panagiotopoulos, Eds. CISM Courses and Lectures No. 302, Springer-Verlag, Wien, New-York.

    Google Scholar 

  • Panagiotopoulos, P.D. (1993). Hemivariational Inequalities: Applications to Mechanics and Engineering, Springer-Verlag, New-York, Boston, Berlin.

    MATH  Google Scholar 

  • Panagiotopoulos, P.D., and Rădulescu, V. (1998). Perturbations of hemivariational inequalities with constraints and applications, Journal of Global Optimization 12: 285–297.

    Article  MATH  Google Scholar 

  • Pleijel, A. (1950). On the eigenvalues and eigenfunctions of elastic plates, Communications in Pure and Applied Mathematics 3: 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  • Rabinowitz, P.H. (1978). Some critical point theorems and applications to semi-linear elliptic partial differential equations, Ann. Sc. Norm. Sup. Pisa 2: 215–223.

    MathSciNet  Google Scholar 

  • Rădulescu, V. (1993). Mountain Pass theorems for non-differentiable functions and applications, Proc. Japan Acad. 69A: 193–198.

    Google Scholar 

  • Szulkin, A., and Willem, M. (1999). Eigenvalue problems with indefinite weight, Studia Mathematica, 135: 191–201.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Craiova, 1100, Craiova, Romania

    Vicenţiu Rădulescu

Authors
  1. Vicenţiu Rădulescu
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, Virginia, USA

    David Y. Gao

  2. Department of Mathematics, University of Glasgow, Glasgow, UK

    Ray W. Ogden

  3. Department of Civil Engineering, Technical University Carolo Wilhelmina, Braunschweig, Germany

    Georgios E. Stavroulakis

Additional information

This paper is dedicated to the memory of Professor P.D. Panagiotopoulos.

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© 2001 Kluwer Academic Publishers

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Rădulescu, V. (2001). Hemivariational Inequalities Associated to Multivalued Problems with Strong Resonance. In: Gao, D.Y., Ogden, R.W., Stavroulakis, G.E. (eds) Nonsmooth/Nonconvex Mechanics. Nonconvex Optimization and Its Applications, vol 50. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0275-9_15

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  • DOI: https://doi.org/10.1007/978-1-4613-0275-9_15

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7973-7

  • Online ISBN: 978-1-4613-0275-9

  • eBook Packages: Springer Book Archive

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