Multiple solutions of hemivariational inequalities with area-type term

Calculus of Variations and Partial Differential Equations

Volumn 10, Issue 4, 2000, Pages 355-387

  Degiovanni, Marco ^a   Marzocchi, Marco ^a   Rǎdulescu, Vicenţiu D ^b  

^a UNIVERSITÀ CATTOLICA DEL SACRO CUORE   (Italy)

^b UNIVERSITY OF CRAIOVA   (Romania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0004330465     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s005269900034     Document Type: Article

References (50)

1. A. Ambrosetti, RH. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381.
2. L. Ambrosio, G. Dal Maso, A general chain rule for distributional derivatives, Proc. Amer. Math. Soc. 108 (1990), 691-702.
3. L. Ambrosio, S. Mortola, V.M. Tortorelli, Functionals with linear growth defined on vector valued BV functions, J. Math. Pures Appl. 70 (1991), 269-323.
4. G. Anzellotti, The Euler equation for functionals with linear growth, Trans. Amer. Math. Soc. 290 (1985), 483-501.
5. M.F. Bocea, Multiple solutions for a class of eigenvalue problems involving a nonlinear monotone operator in hemivariational inequalities, Appl. Anal. 65 (1997), 395-407.
6. H. Brezis, "Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert", North-Holland Mathematics Studies, 5, Notas de Matemàtica (50), North-Holland, Amsterdam-London, 1973.
7. I. Campa, M. Degiovanni, Subdifferential calculus and nonsmooth critical point theory, SIAM J. Optim., in press.
8. A. Canino, Multiplicity of solutions for quasilinear elliptic equations, Topol. Methods Nonlinear Anal. 6 (1995), 357-370.
9. A. Canino, On a jumping problem for quasilinearelliptic equations, Math.Z. 226 (1997), 193-210.
10. A. Canino, M. Degiovanni, Nonsmooth critical point theory and quasilinear elliptic equations, Topological Methods in Differential Equations and Inclusions (Montreal, PQ, 1994), 1-50, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 472, Kluwer Acad. Publ., Dordrecht, 1995.
11. M. Carriero, G. Dal Maso, A. Leaci, E. Pascali, Relaxation of the non-parametric Plateau problem with an obstacle, J. Math. Pures Appl. 67 (1988), 359-396.
12. K.C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80 (1981), 102-129.
13. D.C. Clark, A variant of the Ljusternik-Schnirelmann theory, Indiana Univ. Math.J. 22 (1972), 65-74.
14. F.H. Clarke, "Optimization and Nonsmooth Analysis", Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1983.
15. J.-N. Corvellec, M. Degiovanni, Nontrivial solutions of quasilinear equations via non-smooth Morse theory, J. Differential Equations 136 (1997), 268-293.
16. J.-N. Corvellec, M. Degiovanni, M. Marzocchi, Deformation properties for continuous functionals and critical point theory, Topol. Methods Nonlinear Anal. 1 (1993), 151-171.
17. E. De Giorgi, A. Marino, M. Tosques, Problemi di evoluzione in spazi metrici e curve di massima pendenza, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 68 (1980), 180-187.
18. M. Degiovanni, Nonsmooth critical point theory and applications, Second World Congress of Nonlinear Analysts (Athens, 1996), Nonlinear Anal. 30 (1997), 89-99.
19. M. Degiovanni, M. Marzocchi, A critical point theory for nonsmooth functionals, Ann. Mat. Pura Appl. (4) 167 (1994), 73-100.
20. M. Degiovanni, F. Schuricht, Buckling of nonlinearly elastic rods in the presence of obstacles treated by nonsmooth critical point theory, Math. Ann. 311 (1998), 675-728.
21. M. Degiovanni, S. Zani, Multiple solutions of semilinear elliptic equations with one-sided growth conditions, in "Advanced Topics in Nonlinear Operator Theory", Math. Comput. Modelling, in press.
22. I. Ekeland, R. Temam, "Convex analysis and variational problems", Studies in Mathematics and its Applications, 1, North-Holland Publishing Co., Amsterdam-Oxford, 1976.
23. n, Differential Integral Equations, in press.
24. E. Giusti, "Minimal Surfaces and Functions of Bounded Variation", Birkhäuser, Basel, 1984.
25. D. Goeleven, D. Motreanu, P.D. Panagiotopoulos, Multiple solutions for a class of eigenvalue problems in hemivariational inequalities, Nonlinear Anal. 29 (1997), 9-26.
26. D. Goeleven, D. Motreanu, P.D. Panagiotopoulos, Multiple solutions for a class of hemivariational inequalities involving periodic energy functionals, Math. Methods Appl. Sci. 20 (1997), 547-568.
27. D. Goeleven, D. Motreanu, P.D. Panagiotopoulos, Semicoercive variational-hemivariational inequalities, Appl. Anal. 65 (1997), 119-134.
28. D. Goeleven, D. Motreanu, P.D. Panagiotopoulos, Eigenvalue problems for variational-hemivariational inequalities at resonance, Nonlinear Anal. 33 (1998), 161-180.
29. G. Goffman, J. Serrin, Sublinear functions of measures and variational integrals, Duke Math.J. 31 (1964), 159-178.
30. A. Ioffe, E. Schwartzman, Metric critical point theory I. Morse regularity and homotopic stability of a minimum, J. Math. Pures Appl. (9) 75 (1996), 125-153.
31. A. Ioffe, E. Schwartzman, Metric critical point theory II. Deformation techniques. New Results in Operator Theory and its Applications, 131-144, Oper. Theory Adv. Appl., 98, Birkhäuser, Basel, 1997.
32. G. Katriel, Mountain pass theorems and global homeomorphism theorems, Ann. Inst.H. Poincaré Anal. Non Linéaire 11 (1994), 189-209.
33. D. Kinderlehrer, G. Stampacchia, "An introduction to variational inequalities and their applications", Pure and Applied Mathematics, 88, Academic Press, New York-London-Toronto, Ont., 1980.
34. A. Marino, The calculus of variations and some semilinear variational inequalities of elliptic and parabolic type, Partial Differential Equations and the Calculus of Variations. Volume II. Essays in Honor of Ennio De Giorgi, Birkäuser, Boston, 1989.
35. A. Marino, D. Scolozzi, Geodetiche con ostacolo, Boll. Un. Mat. Ital. B (6) 2 (1983), 1-31.
36. M. Marzocchi, Multiple solutions of quasilinear equations involving an area-type term, J. Math. Anal. Appl. 196 (1995), 1093-1104.
37. M. Marzocchi, Nontrivial solutions of quasilinear equations in BV, Well-posed Problems and Stability in Optimization (Marseille, 1995), Serdica Math.J. 22 (1996), 451-470.
38. D. Motreanu, Z. Naniewicz, Discontinuous semilinear problems in vector-valued function spaces, Differential Integral Equations 9 (1996), 581-598.
39. D. Motreanu, P.D. Panagiotopoulos, A minimax approach to the eigenvalue problem of hemivariational inequalities and applications, Appl. Anal. 58 (1995), 53-76.
40. D. Motreanu, P.D. Panagiotopoulos, Double eigenvalue problems for hemivariational inequalities, Arch. Rational Mech. Anal. 140 (1997), 225-251.
41. Z. Naniewicz, P.D. Panagiotopoulos, "Mathematical Theory of Hemivariational Inequalities and Applications", Monographs and Textbooks in Pure and Applied Mathematics, 188, Marcel Dekker, Inc., New York, 1995.
42. P.D. Panagiotopoulos, "Hemivariational Inequalities. Applications in Mechanics and Engineering", Springer-Verlag, Berlin, 1993.
43. P.D. Panagiotopoulos, V.D. Rǎdulescu, Perturbations of hemivariational inequalities with constraints and applications, J. Global Optim. 12 (1998), 285-297.
44. P.H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differential Equations", CBMS Reg. Conf. Series Math. 65, Amer. Math. Soc., Providence, RI, 1986.
45. Yu.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math.J. 9 (1968), 1039-1045 (translated from Sibirsk. Mat. Zh. 9 (1968), 1386-1394).
46. Yu.G. Reshetnyak, Weak convergence of completely additive vector functions on a set, Siberian Math.J. 9 (1968), 1039-1045 (translated from Sibirsk. Mat. Zh. 9 (1968), 1386-1394).
47. R.T. Rockafellar, Integral functionals, normal integrands and measurable selections, Nonlinear Operators and the Calculus of Variations (Bruxelles, 1975), 157-207, Lecture Notes in Math., 543, Springer, Berlin-New York, 1976.
48. R.T. Rockafellar, Generalized directional derivatives and subgradients of nonconvex functions, Canad.J. Math. 32 (1980), 257-280.
49. M. Struwe, "Variational Methods", Springer-Verlag, Berlin, 1990.
50. A.I. Vol'pert, S.I. Hudjaev, "Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics", Martinus Nijhoff Publisher, Dordrecht, 1985.