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1996 | 35 | 1 | 51-72
Tytuł artykułu

On minimizing noncoercive functionals on weakly vlosed sets

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider noncoercive functionals on a reflexive Banach space and establish minimization theorems for such functionals on smooth constraint manifolds. The functionals considered belong to a class which includes semi-coercive, compact-coercive and P-coercive functionals. Some applications to nonlinear partial differential equations are given.
Rocznik
Tom
35
Numer
1
Strony
51-72
Opis fizyczny
Daty
wydano
1996
Twórcy
autor
  • Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA
  • Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA
Bibliografia
  • [ASV1] D. D. Ang, K. Schmitt and L. K. Vy, Noncoercive variational inequalities: some applications, Nonlinear Analysis, TMA 15(1990), 497-512.
  • [ASV2] D. D. Ang, K. Schmitt and L. K. Vy, Variational inequalities and the contact of elastic plates, in: Differential Equations and Applications in Biology, Physics, and Engineering, Goldstein, Kappel, Schappacher (eds.), M. Dekker, N.Y., 1991,1-19.
  • [ASV3] D.D. Ang, K. Schmitt and L. K. Vy, P-coercive variational inequalities and unilateral problems for von Karman's equations, in: World Scientific Series in Applied Math., vol. 1, R. Agarwal (ed.), World Scientific, Singapore, 1992,15-29.
  • [AV] D. D. Ang and L. K. Vy, Some applications and extensions of P-coercive variational inequalities, preprint(1993).
  • [BGT] G. Baiocchi, F. Gastaldi and F. Tomarelli, Inéquations variationnelles non coercives, C. R. Acad. Sc. Paris 299 (1984), 647-650.
  • [BTW] A. Ben Naoum, C. Troestler and M. Willem, Existence and multiplicity results for homogeneous second order differential equations, J. Diff. Equations 112 (1994), 239-249.
  • [B] V. Brézis, Analyse Fonctionnelle, Masson, Paris 1983.
  • [DL] G. Duvaut and J. L. Lions, Les Inéquations en Mécanique et en Physique, Dunod, Paris, 1972.
  • [F] G. Fichera, Problemi elastostatici con vincoli unilaterali: il problema di Signorini con ambigue condizioni al contorno, Mem. Acc. Naz. Lincei, Ser. 8 vol 7 (1964), 91-140.
  • [GT] F. Gastaldi and F. Tomarelli, Some remarks on nonlinear and noncoercive variational inequalities, Boll. U. M. I. (7) 1-B (1987), 143-165.
  • [H] P. Hess, On nonlinear mappings of monotone type with respect to Banach spaces, Ind. Univ. Math. J. 23 (1974), 645-654.
  • [J] R. C. James, Orthogonality and linear functionals in normed spaces, Trans. Amer. Math. Soc. 61 (1947), 265-292.
  • [KS] D. Kinderlehrer and G. Stampacchia, Introduction to Variational Inequalities, Academic Press, New York, 1980.
  • [K] M. A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon, New York, 1964.
  • [LS] J. L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math. 20 (1967), 493-519.
  • [LS1] V. K. Le and K. Schmitt, Minimization problems for noncoercive functionals subject to constraints, Trans. A. M. S. 347 (1995), 4485-4513.
  • [LS2] V. K. Le and K. Schmitt, Minimization problems for noncoercive functionals subject to constraints II, Advances in Diff. Eq., to appear.
  • [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989.
  • [PS] D. Pascali and J. Sburlan, Nonlinear Mappings of Monotone Type, Sijthoff and Noordhoff, Bucharest, 1978.
  • [PM] M. A. del Pino and R. F. Manasevich, Global bifurcation from the eigenvalues of the p-Laplacian, J. Diff. Equations 92 (1991), 226-251.
  • [R] T. R. Rockafellar, Convex Analysis, Princeton University Press, New Jersey, 1970.
  • [S] M. Schatzman, Problèmes aux limites non linéaires semi-coercifs, C. R. Acad. Sc. Paris 275 (1972), 1305-1308.
  • [St] M. Struwe, Variational Methods and their Applications in Nonlinear Partial Differential Equations, Springer, New York, 1990.
  • [T] S. L. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1971), 173-180.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv35i1p51bwm
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