# On minimizing noncoercive functionals on weakly vlosed sets

Banach Center Publications (1996)

- Volume: 35, Issue: 1, page 51-72
- ISSN: 0137-6934

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topLe, Vy, and Schmitt, Klaus. "On minimizing noncoercive functionals on weakly vlosed sets." Banach Center Publications 35.1 (1996): 51-72. <http://eudml.org/doc/251315>.

@article{Le1996,

abstract = {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.},

author = {Le, Vy, Schmitt, Klaus},

journal = {Banach Center Publications},

keywords = {variational inequalities; P-coercive functional; semi-coercive functional; minimization of functionals; noncoercive functionals; regularization technique; semilinear elliptic problem; quasi-variational inequality},

language = {eng},

number = {1},

pages = {51-72},

title = {On minimizing noncoercive functionals on weakly vlosed sets},

url = {http://eudml.org/doc/251315},

volume = {35},

year = {1996},

}

TY - JOUR

AU - Le, Vy

AU - Schmitt, Klaus

TI - On minimizing noncoercive functionals on weakly vlosed sets

JO - Banach Center Publications

PY - 1996

VL - 35

IS - 1

SP - 51

EP - 72

AB - 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.

LA - eng

KW - variational inequalities; P-coercive functional; semi-coercive functional; minimization of functionals; noncoercive functionals; regularization technique; semilinear elliptic problem; quasi-variational inequality

UR - http://eudml.org/doc/251315

ER -

## References

top- [ASV1] D. D. Ang, K. Schmitt and L. K. Vy, Noncoercive variational inequalities: some applications, Nonlinear Analysis, TMA 15(1990), 497-512. Zbl0735.49007
- [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. Zbl0761.35038
- [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. Zbl0830.49011
- [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. Zbl0808.58013
- [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. Zbl0298.73001
- [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. Zbl0146.21204
- [GT] F. Gastaldi and F. Tomarelli, Some remarks on nonlinear and noncoercive variational inequalities, Boll. U. M. I. (7) 1-B (1987), 143-165. Zbl0624.47053
- [H] P. Hess, On nonlinear mappings of monotone type with respect to Banach spaces, Ind. Univ. Math. J. 23 (1974), 645-654. Zbl0259.47051
- [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. Zbl0152.34601
- [LS1] V. K. Le and K. Schmitt, Minimization problems for noncoercive functionals subject to constraints, Trans. A. M. S. 347 (1995), 4485-4513. Zbl0849.35040
- [LS2] V. K. Le and K. Schmitt, Minimization problems for noncoercive functionals subject to constraints II, Advances in Diff. Eq., to appear. Zbl1020.35025
- [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. Zbl0676.58017
- [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. Zbl0781.35017
- [R] T. R. Rockafellar, Convex Analysis, Princeton University Press, New Jersey, 1970. Zbl0193.18401
- [S] M. Schatzman, Problèmes aux limites non linéaires semi-coercifs, C. R. Acad. Sc. Paris 275 (1972), 1305-1308. Zbl0246.47062
- [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. Zbl0214.12701

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