Non-smooth variational bifurcation
Marco Degiovanni; Antonio Marino
- Volume: 81, Issue: 3, page 259-269
- ISSN: 1120-6330
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topDegiovanni, Marco, and Marino, Antonio. "Non-smooth variational bifurcation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 81.3 (1987): 259-269. <http://eudml.org/doc/287287>.
@article{Degiovanni1987,
abstract = {We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.},
author = {Degiovanni, Marco, Marino, Antonio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Variational bifurcation; non-smooth analysis; variational inequalities; generalized Hessian form; bifurcation; lower semicontinuous functionals},
language = {eng},
month = {9},
number = {3},
pages = {259-269},
publisher = {Accademia Nazionale dei Lincei},
title = {Non-smooth variational bifurcation},
url = {http://eudml.org/doc/287287},
volume = {81},
year = {1987},
}
TY - JOUR
AU - Degiovanni, Marco
AU - Marino, Antonio
TI - Non-smooth variational bifurcation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1987/9//
PB - Accademia Nazionale dei Lincei
VL - 81
IS - 3
SP - 259
EP - 269
AB - We consider bifurcation problems associated with some lower semicontinuous functionals that do not satisfy the usual regularity assumptions. For such functionals it is possible to define a generalized "Hessian form" and to show that certain eigenvalues of this one are bifurcation values. The results are applied to a bifurcation problem for elliptic variational inequalities.
LA - eng
KW - Variational bifurcation; non-smooth analysis; variational inequalities; generalized Hessian form; bifurcation; lower semicontinuous functionals
UR - http://eudml.org/doc/287287
ER -
References
top- BENCI, V. and MICHELETTI, A.M. (1975) - Su un problema di autovalori per disequazioni variazionali, «Ann. Mat. Pura Appl.», (4), 107, 359-371. Zbl0324.49004MR412941
- BERGER, M.S. (1967) - On von Karman's equations and the buckling of a thin elastic plate, I the clamped plate, «Comm. Pure Appl. Math.», 20, 687-719. Zbl0162.56405MR221808
- BERGER, M.S. and FIFE, P.C. (1968) - Von Karman's equations and the buckling of a thin elastic plate, II plate with general edge conditions, «Comm. Pure Appl. Math.», 21, 227-241. Zbl0162.56501MR229978
- BOHME, R. (1972) - Die Lösung der Verzweigungsgleichungen für nichtlineare Eigenwertprobleme, «Math. Z.», 127, 105-126. Zbl0254.47082MR312348
- BREZIS, H. (1973) - Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, Notas de Matemàtica (50), North-Holland, Amsterdam-London. Zbl0252.47055MR348562
- CHOBANOV, G., MARINO, A. and SCOLOZZI, D. (1986) - Autovalori dell'operatore di Laplace rispetto ad un ostacolo e relativa equazione di evoluzione, «Dip. Mat. Pisa», 166, Pisa.
- CHOBANOV, G., MARINO, A. and SCOLOZZI, D. (1986) - Molteplicità dei punti stazionari per una classe di funzioni semicontinue. Condizioni di "non tangenza" fra dominio della funzione e vincolo. Pendenza e regolarizzazione, «Dip. Mat. Pisa», 167, Pisa.
- CLARKE, F.H. (1983) - Optimization and non-smooth analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York. Zbl0582.49001MR709590
- DE GIORGI, E., DAL MASO, G. and LONGO, P. (1980) - -limiti di ostacoli, «Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», (8) 68, 481-487. Zbl0512.49011MR639976
- DE GIORGI, E., DE GIOVANNI, M., MARINO, A. and TOSQUES, M. (1983) - Evolution equations for a class of nonlinear operators, «Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», (8) 75, 1-8. Zbl0597.47045MR780801
- DE GIORGI, E. and FRANZONI, T. (1975) - Su un tipo di convergenza variazionale, «Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», (8) 58, 842-850. Zbl0339.49005MR448194
- DE GIORGI, E., MARINO, A. and TOSQUES, M. (1980) - Problemi di evoluzione in spazi metrici e curve di massima pendenza, «Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», (8), 68, 180-187. Zbl0465.47041MR636814
- DE GIORGI, E., MARINO, A. and TOSQUES, M. (1982) - Funzioni -convesse, «Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.», (8), 73, 6-14 (1983). Zbl0521.49011MR726279
- DEGIOVANNI, M. and MARINO, A. (1986) - Bifurcation for some nonlinear elliptic variational inequalities, Variational Methods in Differential Problems (Trieste, 1985), «Rend. Istit. Mat. Univ. Trieste», 18, 40-48. Zbl0636.35009MR898392
- DE GIOVANNI, M., MARINO, A. and TOSQUES, M. (1985) - Evolution equations with lack of convexity, «Non linear Anal.», 9, 1401-1443. Zbl0545.46029MR820649DOI10.1016/0362-546X(85)90098-7
- DO, C. (1976) - The buckling of a thin elastic plate subjected to unilateral conditions, Applications of methods of functional analysis to problems in mechanics (Joint Sympos., IUTAM/IMU, Marseille, 1975), 307-316, «Lecture Notes in Math.», 503, Springer, Berlin. Zbl0337.73034MR669061
- FADELL, E.R. and RABINOWITZ, P.H. (1977) - Bifurcation for odd potential operators and an alternative topological index, «J. Funct. Anal.», 26, 48-67. Zbl0363.47029MR448409
- KINDERLEHRER, D. and STAMPACCHIA, G. (1980) - An introduction to variational inequalities and their applications, «Pure and Applied Mathematics», 88, Academic Press, New York-London-Toronto, Ont. Zbl0457.35001MR567696
- KRASNOSELSKII, M.A. (1964) - Topological methods in the theory of nonlinear integral equations, Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow, 1956. The Macmillan Co., New York. MR159197
- KUČERA, M., NEČAS, J. and SOUČEK, J. (1978) - The eigenvalue problem for variational inequalities and a new version of the Ljusternik-Schnirelmann theory. Nonlinear analysis (collection of papers in honor of Erich H. Rothe), 125-143, Academic Press, New York. Zbl0463.47041MR513782
- MARINO, A. (1973) - La biforcazione nel caso variazionale, «Confer. Sem. Mat. Univ. Bari», 132. Zbl0323.47046MR348570
- MARINO, A. and SCOLOZZI, D. (1983) - Geodetiche con ostacolo, «Boll. Un. Mat. Ital.», B(6), 2, 1-31. Zbl0563.53034MR698480
- McLEOD, J.B. and TURNER, R.E.L. (1976) - Bifurcation for non-differentiable operators with an application to elasticity, «Arch. Rational Mech. Anal.», 63, 1-45. Zbl0356.47030MR473953
- RABINOWITZ, P.H. (1971) - Some global results for nonlinear eigenvalue problems, «J. Funct. Anal.», 7, 487-513. Zbl0212.16504MR301587
- RABINOWITZ, P.H. (1977) - A bifurcation theorem for potential operators, «J. Funct. Anal.», 25, 412-424. Zbl0369.47038MR463990
- RIDDELL, R.C. (1979) - Eigenvalue problems for nonlinear elliptic variational inequalities, «Nonlinear Anal.», 3, 1-33. Zbl0416.49009MR520467DOI10.1016/0362-546X(79)90030-0
- SZULKIN, A. (1985) - Positive solutions of variational inequalities: a degree-theoretic approach, «J. Differential Equations», 57, 90-111. Zbl0535.35029MR788424DOI10.1016/0022-0396(85)90072-5
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