| Title:
|
Bifurcation of stationary solutions to quasivariational inequalities (English) |
| Author:
|
Bosák, Miroslav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
119 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
21-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
unilateral problems |
| Keyword:
|
quasivariational inequalities |
| Keyword:
|
variational inequalities |
| Keyword:
|
eigenvalue problems |
| Keyword:
|
partial differential inequalities |
| Keyword:
|
unilateral problems |
| MSC:
|
35B32 |
| MSC:
|
35J85 |
| MSC:
|
47H15 |
| MSC:
|
47H19 |
| MSC:
|
49J40 |
| idZBL:
|
Zbl 0808.35039 |
| idMR:
|
MR1303549 |
| DOI:
|
10.21136/MB.1994.126204 |
| . |
| Date available:
|
2009-09-24T21:02:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126204 |
| . |
| Reference:
|
[1] J. P. Aubin A. Cellina: Differential Inclusions.Springer-Velag, Berlin, 1984. MR 0755330 |
| Reference:
|
[2] C. Baiocchi A. Capelo: Disequazioni variazionali e quazivariazionali.Applicazioni a problemi di frontiera libera. Pitagora Editrice, Bologna, 1978. |
| Reference:
|
[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. |
| Reference:
|
[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 |
| Reference:
|
[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. |
| Reference:
|
[6] M. Degiovanni A. Marino: Non-smooth variational bifurcation.Atti Acc. Lincei Rend. Fis. 8, LXXXI (1987), 259-270. MR 0999818 |
| Reference:
|
[7] A. Friedman: A class of parabolic quasi-variatinal inequalities, II.J. Diff. Eq. 22 (1976), 379-401. MR 0437930, 10.1016/0022-0396(76)90035-8 |
| Reference:
|
[8] S. Fučík A. Kufner: Nonlinear Differential Equations.Elsevier, Amsterdam, 1980. MR 0558764 |
| Reference:
|
[9] S. Fučík J. Nečas J. Souček V. Souček: Spectral analysis of nonlinear operators.Lecture Notes in Mathematics 346, Springer, Berlin, 1973. MR 0467421 |
| Reference:
|
[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. MR 0551113, 10.1016/0022-1236(79)90028-4 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[13] M. Kučera: Bifurcation points of variational inequalities.Czechoslovak Math. J. 32 (107) (1982), 208-226. MR 0654057 |
| Reference:
|
[14] J. L. Lions E. Magenes: Problèmes aux limites non homogènes.Dunod, Paris, 1968. |
| Reference:
|
[15] E. Miersemann: Über höhere Verzweigungspunkte nichtlinearen Variationsungleichungen.Math. Nachr. 85 (1978), 195-213. MR 0517651, 10.1002/mana.19780850116 |
| Reference:
|
[16] E. Miersemann: On higher eigenvalues of variational inequalities.Comment. Math. Univ. Carol. 24 (1983), 657-665. Zbl 0638.49020, MR 0738561 |
| Reference:
|
[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 |
| Reference:
|
[18] L. Nirenberg: Topics in Nonlinear Functional Analysis.Courant Institut, New York, 1974. Zbl 0286.47037, MR 0488102 |
| Reference:
|
[19] P. Quittner: Solvability and multiplicity results for variational inequalities.Comment. Math. Univ. Carolin. 30 (1989), no. 3, 579-585. Zbl 0698.49004, MR 1014128 |
| Reference:
|
[20] P. Quittner: Spectral analysis of variational inequalities.Comment. Math. Univ. Carol. 27 (1986), 605-629. MR 0873631 |
| . |
