Recession mappings and noncoercive variational inequalities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 9, 1996, Pages 1573-1603

  Adly, Samir ^a   Goeleven, Daniel ^a,b   Théra, Michel ^a  

^a UNIVERSITY OF LIMOGES   (France)

^b UNIVERSITY OF NAMUR   (Belgium)

Author keywords

Elastic plate; Maximal monotone operator; Navier Stokes equations; Noncoercive variational inequality; Puffed up membrane; Recession function; Subdifferential operator; Unilateral buckling

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; MATHEMATICAL MODELS; SET THEORY; TOPOLOGY;

MAXIMAL MONOTONE OPERATOR; RECESSION MAPPINGS; SOLVABILITY; SUBDIFFERENTIAL OPERATOR; VARIATIONAL INEQUALITIES;

VARIATIONAL TECHNIQUES;

EID: 0030151730     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00364-N     Document Type: Article

References (33)

1. BRÉZIS H. Equations et inéquations non-linéaries dans les espaces vectoriels en dualité, Annls Inst. Fourier Univ. Grenoble 18(1), 115-175 (1968).
2. BROWDER F., Nonlinear monotone operators and convex sets in Banach spaces, Bull. Am. math. Soc. 71, 780-785 (1965).
3. BROWDER F., Nonlinear maximal monotone mappings in Banach spaces, Math. Ann. 175, 81-113 (1968).
4. BROWDER F., Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., Vol 18, Part 2 (the entire issue). Am. Math. Soc., Providence, RI (1976).
5. MOSCO U., A remark on a theorem of F. E. Browder, J. Math. Analysis Applic 20, 90-93 (1967).
6. DUVAULT G. LIONS J.-L., Les Inéquations en Mécanique et en physique. Dunod, Paris (1972).
7. PANAGIOTOPOULOS P. D., Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions. Birkhäuser, Basel (1985).
8. GOELEVEN D., On the solvability of linear noncoercive variational inequality in separable Hilbert spaces, J. Optim. Theory. Applic. 79, (1993).
9. GOELEVEN D. & THÉRA M., Variational inequality and the existence of equilbrium state on a thin elastic plate, Serdica Math. J. 21, 1001-1017 (1995).
10. GOELEVEN D. & THÉRA M., Some Global Results for Nonlinear Eigenvalue Problems Governed by a Variational Inequality of von Karman Type, Univ. Degli Studi di Milano, Quadeno 21, Univ. Degli Studi di Milano, Milan (1993).
11. GOELEVEN D., NGUYEN V. H. & THÉRA M., Méthode du degré et branches de bifurcation dans des inequalities du type de von Karman C. r. Acad. Sci. Paris 317, Série I, 631-635 (1993).
12. GOELEVEN D., NGUYEN V. H. & THÉRA M., Nonlinear eigenvalue problem governed by variational inequality of von Karman type: a degree theoric approach, Topological Methods in Nonlinear Analysis, Vol. 2, pp. 235-276 (1993).
13. GOELEVEN & NGUYEN V. H., On the nonlinear elastohydrodynamic lubrication problem, Bull. Aust. math. Soc. (to appear).
14. ATTOUCH H., CHBANI Z. & MOUDAFI A., Recession Operators and Solvability of Variational Problems. (Preprint, Laboratoire d'Analyse Convexe, Université de Montpellier II) (1993).
15. ATTOUCH H., CHBANI Z. & MOUDAFI A., Recession operators and solvability of variational problems in reflexive Banach spaces (to appear).
16. BAIOCCHI C., BUTTAZZO G., GASTALDI F. & TOMARELLI F., General existence theorems for unilateral problems in continum mechanics, Archs ration. Mech. analysis 100(2), 149-180 (1988).
17. QUITTNER P., Solvability and multiplicity results for variational inequalities, Comment. math. Univ. Carol. 30, 281-302 (1987).
18. SZULKIN A., Positive solution of variational inequalities: A degree theoretical approach, J. diff. Eqns 57, 90-11 (1985).
19. SZULKIN A., Minimax principle for lower semicontinuous functions and applications to nonlinear boundary value problems, Annls Inst. H. Poincaré Analyse nonlinéare 3(2), 77-109 (1986).
20. GOELEVEN D., NGUYEN V. H. WILLEM M., Existence and multiplicity results for noncoercive unilateral problems, Bull. Aust. math. Soc. 49, 489-498 (1994).
21. BAIOCCHI C., GASTALDI F. & TOMARELLI F., Inéquations variationnelles non coercives, C. r. Acad. Sci. Paris 1229, 647-650 (1984).
22. BAIOCCHI C., GASTALDI F. & TOMARELLI F., Some existence results on noncoercive variational inequalities, Annali Scu. norm. sup. Pisa 13, 617-659 (1986).
23. BUTTAZZO G. & TOMARELLI F., Compatibility conditions for nonlinear Neumann problems, Adv. Math. 89, 127-143 (1991).
24. TOMARELLI F., Noncoercive variational inequalities for pseudomonotone operators (Preprint) (1993).
25. ROCKAFELLAR R. T., Convex analysis. Princeton University Press, Princeton NJ (1970).
26. BREZIS H. & NIRENBERG L., Characterizations of ranges of some nonlinear operators and applications to boundary value problems, Annali Scu. norm. Sup. Pisa 225-325 (1978).
27. ZEIDER E., Nonlinear Functional Analysis and its Application II/B, Nonlinear Monotone Operators. Springer, Berlin (1990).
28. ROCKAFELLAR R. T., On the maximal monotonicity of sums of nonlinear monotone operators, Trans. Amr. math. Soc. 149, 75-88 (1970).
29. BRÉZIS H. & HARAUX A., Image d'une somme d'opérateurs monotones et applications, Israel J. Math. 23(2), 165-186 (1976).
30. PAZY A., Semigroups of Nonlinear Operators and Application to Partial Differential Equations, Appl. Math. Sci. Vol. 44. Springer, Berlin (1983).
31. LANDESMAN E. M. & LAZER A. C., Nonlinear pertubations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, 609-623 (1979).
32. BOCCARDO L., DRABEK P. & KUCERA M., Landesman-Lazer conditions for strongly nonlinear boundary value problems, Comment. math. Univ. Carol. 30(3), 411-427 (1989).
33. TEMAM R., Navier-Stokes Equations, Studies in Mathematics and its Applications. North-Holland, Amsterdam (1977).