Some variational theorems of mixed type and elliptic problems with jumping nonlinearities
Antonio Marino; Claudio Saccon
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)
- Volume: 25, Issue: 3-4, page 631-665
- ISSN: 0391-173X
Access Full Article
topHow to cite
topMarino, Antonio, and Saccon, Claudio. "Some variational theorems of mixed type and elliptic problems with jumping nonlinearities." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.3-4 (1997): 631-665. <http://eudml.org/doc/84308>.
@article{Marino1997,
author = {Marino, Antonio, Saccon, Claudio},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {3-4},
pages = {631-665},
publisher = {Scuola normale superiore},
title = {Some variational theorems of mixed type and elliptic problems with jumping nonlinearities},
url = {http://eudml.org/doc/84308},
volume = {25},
year = {1997},
}
TY - JOUR
AU - Marino, Antonio
AU - Saccon, Claudio
TI - Some variational theorems of mixed type and elliptic problems with jumping nonlinearities
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 25
IS - 3-4
SP - 631
EP - 665
LA - eng
UR - http://eudml.org/doc/84308
ER -
References
top- [1] H. Amann - P. Hess, A multiplicity result for a class of elliptic boundary value problems, Proc. Roy. Soc. EdinburghA84 (1979), 145-151. Zbl0416.35029MR549877
- [2] H. Amann - E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa7 (1980), 539-603. Zbl0452.47077MR600524
- [3] A. Ambrosetti, Elliptic equations with jumping nonlinearities, J. Math and Physics18 (1984), 1-12. Zbl0589.35043MR755462
- [4] A. Ambrosetti - G. Prodi, On the inversion of some differential mappings with singularities between Banach spaces, Annals of Mathematics4 (93) (1972), 231-247. Zbl0288.35020MR320844
- [5] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Functional Analysis14 (1973), 349-381. Zbl0273.49063MR370183
- [6] A. Bahri, Résolution générique d'une équation semilinéaire, C. R. Acad. de Sci. Paris Sér. A-B2911980. Zbl0461.35037MR591743
- [7] M. Berger - E. Podolac, On the solutions ofa nonlinear Dirichlet problem, Indiana Univ. Math. J.24 (1975), 837-846. Zbl0329.35026
- [8] C. Bertocchi - M. Degiovanni, On the existence of two branches of bifurcation for eigenvalue problems associated with variational inequalities, in Scritti in onore di Giovanni Melfi, volume 11 of Sci. Mat., pages 35-72. Vita e Pensiero, Milano, 1994. Zbl0828.58007MR1300030
- [9] G. Bordigia, Problemi Perturbativi in Teoria dei punti Critici, Master's thesis, Università Cattolica del Sacro Cuore, Fac. S.M.F.N., Brescia, Feb. 1996.
- [10] N.P. Cac, On trivial solutions of a Dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue, J. Diff. Equations80 (1989), 379-404. Zbl0713.35036MR1011156
- [11] N.P. Cac, On a boundary value problem with nonsmooth jumping nonlinearity, J. Diff. Equations93 (1991), 238-259. Zbl0768.35031MR1125219
- [12] K. Chang, "Infinite Dimensional Morse Theory and Multiple Solution Problems", volume 6 of Progress in Nonlinear Differential Equations and TheirApplications Birckhäuser, Boston, Basel, Berlin, 1991. Zbl0779.58005
- [13] D.G. Costa - D.G. De Figueireido - P.N. Srikanth, The exact number of solutions for a class of ordinary differential equations through Morse index theory, J. Diff. Equations96 (1992), 185-199. Zbl0764.34013MR1153315
- [14] E.N. Dancer, On the Dirichlet problem for weak nonlinear elliptic partial differential equations, Proc. Roy. Soc. EdinburghA76 (1977), 283-300. Zbl0351.35037MR499709
- [15] E.N. Dancer, On the ranges of certain weakly nonlinear partial differential equations, Journal de Mathématiques Pures et Appliquées57 (1978), 351-366. Zbl0394.35040MR524624
- [16] E.N. Dancer, Multiple solutions of asymptotically homogeneous problems, Annals of Mathematics f57 (1988), 63-78. Zbl0850.35043MR980972
- [17] E.N. Dancer, A counterexample to the Lazer-McKenna conjecture, Nonlinear Anal., Theory, Methods and Applications13 (1989), 19-21. Zbl0691.35039MR973364
- [18] E.N. Dancer, Generic domain dependence for nonsmooth equations and the open set problem for jumping nonlinearities, Topological Meth. Nonlinear Anal.1 (1993), 139-150. Zbl0817.35026MR1215262
- [19] D.G. De Figueireido - J.P. Gossez, On the First Curve of the Fuik Spectrum of an Elliptic Operator, preprint, 1994. MR1269657
- [20] S Fučik, Nonlinear equations with noninvertible linear part, Czechoslovak Math. J.24 (1974), 467-495. Zbl0315.47038MR348568
- [21] S Fučik, Boundary value problems with jumping nonlinearities, Căsopis Ešt. Mat.101 (1976), 69-87. Zbl0332.34016MR447688
- [22] T. Gallouet - O. Kavian, Résultats d' existence et de non existence de solutions pour certain problèmes demi-linéaire à l' infini, Ann. Fac. Sci. Toulouse3 (1981), 201-246. Zbl0495.35001MR658734
- [23] J.A. Hempel, Multiple solutions for a class of nonlinear boundary value problems, Indiana Univ. Math. J.20 (1971), 983-996. Zbl0225.35045MR279423
- [24] H. Hofer, Variational and topological methods in partially ordered Hilbert spaces, Math. Ann.261 (1982), 493-514. Zbl0488.47034MR682663
- [25] J.L. Kazdan - F.W. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.28 (1975), 567-597. Zbl0325.35038MR477445
- [26] A.C. Lazer - P.J. M, On the number of solutions of a nonlinear Dirichlet problem, J. Math. Anal. Appl.84 (1981), 282-294. Zbl0496.35039MR639539
- [27] A.C. Lazer - P.J. M, On a conjecture related to the number of solutions of a nonlinear Dirichlet problem, Proc. Roy. Soc. Edinburgh95 (1983), 275-283. Zbl0533.35037MR726879
- [28] A.C. Lazer - P.J. M, Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues I, Comm. in Partial Differential Equations10 (1985), 107-150. Zbl0572.35036MR777047
- [29] A.C. Lazer - P.J. M, Critical point theory and boundary value problems with nonlinearities crossing multiple eigenvalues II, Comm. in Partial Differential Equations11 (1986), 1653-1676. Zbl0654.35082MR871108
- [30] J. Liu, Bifurcation for potential operators, Nonlinear Anal., Theory, Methods and Applications4 (1990), 345-353. Zbl0705.47052MR1066391
- [31] L. Lusternik - L. Schnirelmann, "Méthodes Topologiques dans le Problèmes Variationelles", Hermann, Paris, 1934 Zbl0011.02803
- [32] C.A. Magalhaes, Semilinear elliptic problems with crossing of multiple eigenvalues, Comm. in Partial Differential Equations15 (1990), 1265-1292. Zbl0726.35044MR1077275
- [33] A. Marino - A. Micheletti - A. Pistoia, Some variational results on semilinear problems with asymptotically nonsymmetric behaviour, in Nonlinear Analysis, A Tribute in Honour of Giovanni Prodi, pages 243-256. S. N. S.Pisa, 1991. Zbl0849.35035MR1205387
- [34] A. Marino - A. Micheletti - A. Pistoia, A nonsymmetric asymptotically linear elliptic problem, Topological Meth. Nonlinear Anal.4 (1994), 289-339. Zbl0844.35035MR1350975
- [35] A. Marino - A. Micheletti - A. Pistoia, Sul numero e anche sulla molteplicita delle soluzioni di alcuni problemi ellittici asintoticamente lineari e non simmetrici, in Proceedings of the congress: "Variational Methods in Nonlinear Analysis and Differential Equations" held in Genova, June 1993, pages 123-141. E.C.I.G., 1994.
- [36] A. Marino - A. Micheletti - A. Pistoia, On some elliptic asymptotically linear and nonsymmetric problems, Atti Sem. Mat. Fis. Univ. ModenaXLIII (1995), 401-423. Zbl0859.35034MR1366069
- [37] A. Marino - D. Passaseo, A jumping behaviour induced by an obstacle, in M. GIRARDI - M. MATZEU - F. PACELLA (Editors) Progress in Variational Methods in Hamiltonian Systems and Elliptic Equations, pages 127-143. Pitman, 1992. Zbl0818.35034MR1176349
- [38] A. Marino - C. Saccon, Alcuni teoremi variazionali di tipo misto e un problema ellittico asintoticamente asimmetrico, Atti Sem. Mat. Fis. Univ. Modena, to appear.
- [39] A. Micheletti, A remark on the resonance set for a semilinear elliptic equation, Proc. Roy. Soc. EdinburghA124 (1994), 803-809. Zbl0808.35036MR1298593
- [40] A. Micheletti - A. Pistoia, A variational viewpoint on the existence of three solutions for some elliptic problems, Differential and Integral Equations6 (1995), 67-80. Zbl0852.35049MR1391945
- [41] A. Micheletti - A. Pistoia, A note on the resonance set for a semilinear elliptic equation and an application to jumping nonlinearities, Topological Meth. Nonlinear Anal.9 (5) (1996), 1029-1042. Zbl0851.35042MR1392093
- [42] M. Morse - S.S. Cairns, "Critical Point Theory in Global Analysis and Differential Topology ", Academic Press, New York, 1969. Zbl0177.52102MR245046
- [43] R. Palais, Morse theory on Hilbert manifolds, Topology2 (1963), 299-340. Zbl0122.10702MR158410
- [44] P.H. Rabinowitz, "Minimax Methods in Critical Point Theory with Applications to Differentia Equations " volume 65 of Regional Conference Series in Mathematics, American Matehmatical Society, Providence, R. I., 1986. Zbl0609.58002MR845785
- [45] M. Ramos, A critical point theorem suggested by an elliptic problem with asymmetric nonlinearities, preprint. Zbl0853.58032MR1365232
- [46] B. Ruf, On linear elliptic problems with jumping nonlinearities, Annals of Mathematics4 (1981), 133-151. Zbl0475.35046MR640779
- [47] B. Ruf, Remarks and generalizations related to a recent result ofA, Lazer and P. J. McKennaNonlinear Anal., Theory, Methods and Applications9 (1985), 1325-1330. Zbl0626.34017MR820643
- [48] M. Schechter - K. Tintarev, Pairs of critical points produced by linking subsets with application to semilinear elliptic problems, Bull. Soc. Math. Belg. B44 (1992), 249-261. Zbl0785.58017MR1314040
- [49] S. Solimini, Existence of a third solution for a class of b. p. v. with jumping nonlinearities, Nonlinear Anal., Theory, Methods and Applications7 (1983), 917-927. Zbl0522.35045MR709044
- [50] S. Solimini, Some remarks on the number of solutions of some semilinear elliptic problems, Ann. Inst. Henri Poincaré2 (1985), 143-156. Zbl0583.35044MR794004
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.