Article
Full entry |
PDF
(1.9 MB)
Feedback
PDF
(1.9 MB)
Feedback
Keywords:
unilateral problems; quasivariational inequalities; variational inequalities; eigenvalue problems; partial differential inequalities; unilateral problems
unilateral problems; quasivariational inequalities; variational inequalities; eigenvalue problems; partial differential inequalities; unilateral problems
Summary:
Bifurcation and eigenvalue theorems are proved for a certain type of quasivariational inequalities using the method of a jump in the Leray-Schauder degree.
References:
[1] J. P. Aubin A. Cellina: Differential Inclusions. Springer-Velag, Berlin, 1984. MR 0755330
[2] C. Baiocchi A. Capelo: Disequazioni variazionali e quazivariazionali. Applicazioni a problemi di frontiera libera. Pitagora Editrice, Bologna, 1978.
[3] A. Bensoussan: Inéquations quasivariationelles et contrôle impulsionel. Atti Giorn. Analisi Convessa e Applicazioni (Roma, 1974), (21-26), Quad. gruppi ric. mat. C N. R.,. Univ. Roma, Roma.
[4] A. Bensoussan M. Goutsat. J. L. Lions: Contrôle impulsionel et inéquations quasivariationelles stationnaires. C R. Ac. Sci. Paris 276 (1973), 1279-1284. MR 0317144
[5] M. Kučera M. Bosák: Bifurcation for quasivariational inequalities of reaction-diffusion type. Proceedings of the international conference on differential equations and mathematical modelling Equam, Varenna 1992.
[6] M. Degiovanni A. Marino: Non-smooth variational bifurcation. Atti Acc. Lincei Rend. Fis. 8, LXXXI (1987), 259-270. MR 0999818
[7] A. Friedman: A class of parabolic quasi-variatinal inequalities, II. J. Diff. Eq. 22 (1976), 379-401. DOI 10.1016/0022-0396(76)90035-8 | MR 0437930
[8] S. Fučík A. Kufner: Nonlinear Differential Equations. Elsevier, Amsterdam, 1980. MR 0558764
[9] S. Fučík J. Nečas J. Souček V. Souček: Spectral analysis of nonlinear operators. Lecture Notes in Mathematics 346, Springer, Berlin, 1973. MR 0467421
[10] J. Joly U. Mosco: A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationelles. J. Functional Anal. 34 (1979), 107-137. DOI 10.1016/0022-1236(79)90028-4 | MR 0551113
[11] M. Kučera: A new method for obtaining eigenvalues of variational inequalities based on bifurcation theory. Čas. pěst. mat. 104 (1979), 389-411. MR 0553173
[12] M. Kučera: A new method for obtaining eigenvalues of variational inequalities. Operators with multiple eigenvalues. Czechoslovak Math. J. 32(1982), 197-207. MR 0654056
[13] M. Kučera: Bifurcation points of variational inequalities. Czechoslovak Math. J. 32 (107) (1982), 208-226. MR 0654057
[14] J. L. Lions E. Magenes: Problèmes aux limites non homogènes. Dunod, Paris, 1968.
[15] E. Miersemann: Über höhere Verzweigungspunkte nichtlinearen Variationsungleichungen. Math. Nachr. 85 (1978), 195-213. DOI 10.1002/mana.19780850116 | MR 0517651
[16] E. Miersemann: On higher eigenvalues of variational inequalities. Comment. Math. Univ. Carol. 24 (1983), 657-665. MR 0738561 | Zbl 0638.49020
[17] U. Mosco: Implicit variational problems and quasivariational inequalities. Nonlinear operators and the calculus of variations (Summer School, Univ. Libre Bruxelles, Brussels, 1975), Lecture Notes in Math., vol. 543. Springer, Berlin, 1976 83-156. MR 0513202
[18] L. Nirenberg: Topics in Nonlinear Functional Analysis. Courant Institut, New York, 1974. MR 0488102 | Zbl 0286.47037
[19] P. Quittner: Solvability and multiplicity results for variational inequalities. Comment. Math. Univ. Carolin. 30 (1989), no. 3, 579-585. MR 1014128 | Zbl 0698.49004
[20] P. Quittner: Spectral analysis of variational inequalities. Comment. Math. Univ. Carol. 27 (1986), 605-629. MR 0873631
Search
Partner of
