Some remarks on the number of solutions of some nonlinear elliptic problems
Annales de l'I.H.P. Analyse non linéaire (1985)
- Volume: 2, Issue: 2, page 143-156
- ISSN: 0294-1449
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topSolimini, Sergio. "Some remarks on the number of solutions of some nonlinear elliptic problems." Annales de l'I.H.P. Analyse non linéaire 2.2 (1985): 143-156. <http://eudml.org/doc/78092>.
@article{Solimini1985,
author = {Solimini, Sergio},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {bifurcation from infinity; multiplicity; eigenvalues of the Laplacian},
language = {eng},
number = {2},
pages = {143-156},
publisher = {Gauthier-Villars},
title = {Some remarks on the number of solutions of some nonlinear elliptic problems},
url = {http://eudml.org/doc/78092},
volume = {2},
year = {1985},
}
TY - JOUR
AU - Solimini, Sergio
TI - Some remarks on the number of solutions of some nonlinear elliptic problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1985
PB - Gauthier-Villars
VL - 2
IS - 2
SP - 143
EP - 156
LA - eng
KW - bifurcation from infinity; multiplicity; eigenvalues of the Laplacian
UR - http://eudml.org/doc/78092
ER -
References
top- [1] A. Ambrosetti and G. Prodi, On the inversion of some differential mapping with singularities between Babach spaces. Ann. Mat. Pura Appl., t. 93, 1973, p. 231-247. Zbl0288.35020MR320844
- [2] M. Berger and E. Podolac, On the solutions of a nonlinear Dirichlet Problem. Indiana Univ. Math. J., t. 24, 1975, p. 837-846. Zbl0329.35026MR377274
- [3] S. Fucik, Remarks on a result by A. AMBROSETTI and G. PRODI. Boll. U. M. I., t. 11, 1975, p. 259-267. Zbl0303.35037MR382849
- [4] H. Berestycki, Le nombre de solutions de certains problèmes semilinéaires elliptiques. J. Funct. An., t. 40, 1981, p. 1-29. Zbl0452.35038MR607588
- [5] J.L. Kazdan and F.W. Warner, Remarks on some quasilinear elliptic equations. Comm. Pure. Appl. Math., t. 28, 1975, p. 567-597. Zbl0325.35038MR477445
- [6] E.N. Dancer, On the ranges of certain weakly nonlinear elliptic partial differential equations. J. Math. Pures et Appl., t. 57, 1978, p. 351-366. Zbl0394.35040MR524624
- [7] H. Amann and P. Hess, A multiplicity result for a class of elliptic boundary value problems. Proc. Ac. Soc. Ed., t. 84 A, 1979, p. 145-151. Zbl0416.35029MR549877
- [8] D.G. De Figueiredo, On the superlinear Ambrosetti-Prodi problems. Nonlin. An. TMA, t. 8, 1984, p. 655-665. Zbl0554.35045MR746723
- [9] D.G. De Figueiredo and S. Solimini, A variational approach to superlinear elliptic problems. Comm. PDE, t. 9, 1984, p. 699. Zbl0552.35030MR745022
- [10] A.C. Lazer and P.J. Mckenna, On the number of solutions of a nonlinear Dirichlet problem. J. of Math. Analysis and Applications, t. 84, 1981, p. 282-294. Zbl0496.35039MR639539
- [11] S. Solimini, Existence of a third solution for a class of b. v. p. with jumping non-linearities. Nonlin. An. TMA t. 7, no. 8, 1983, p. 917-927. Zbl0522.35045MR709044
- [12] A. Ambrosetti, Elliptic equations with jumping nonlinearities. J. Math. Phys. Sci. (to appear). Zbl0589.35043MR755462
- [13] H. Hofer, Variational and topological methods in partially ordered Hilbert spaces. Math. Annalen, t. 261, 1982, p. 493-514. Zbl0488.47034MR682663
- [14] A.C. Lazer and P.J. Mckenna, Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems. J. Math. Analysis and Applications (to appear). Zbl0584.35053MR787722
- [15] A.C. Lazer and P.J. Mckenna, On a conjecture related to the number of the solutions of a nonlinear Dirichlet problem, to appear Proc. Roy. Soc. Edinburgh. Zbl0533.35037
- [16] E. Podolak, On the range operator equations with an asymptotically nonlinear term. Indiana Univ. Math. J., t. 25, 1976, p. 1127-1137. Zbl0353.47035MR425698
- [17] T. Gallouet and O. Kavian, Résultats d'existence et de non existence de solutions pour certains problèmes demi-linéaires à l'infini. Ann. Fac. Sc. de Toulouse, 1981. Zbl0495.35001
- [18] B. Ruf, On nonlinear elliptic problems with jumping nonlinearities. Ann. Mat. Pure e Appl. Serie IV, t. CXXVIII, 1981, p. 133-151. Zbl0475.35046MR640779
- [19] Adimurthi and P.N. Srikanth, On the exact number of solutions at infinity for Ambrosetti-Prodi class of problems, preprint. Zbl0589.35048
- [20] S. Solimini, Multiplicity results for a nonlinear Dirichlet problem. Proc. Royal Soc. Edinburgh, t. 96 A, 1984. Zbl0557.35052MR760781
- [21] A.C. Lazer and P.J. Mckenna, Multiplicity results for a semi-linear boundary value problem with the nonlinearity crossing higher eigenvalues, preprint. Zbl0582.35049MR1237124
- [22] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, 1980. Zbl0457.35001MR567696
- [23] E.N. Dancer, On the Dirichlet problem for weakly nonlinear elliptic partial differential equations. Proc. Roy. Soc. Edinburgh, t. 76 A, 1977, p. 283-300. Zbl0351.35037MR499709
- [24] M.A. Krasnosel'skii, Topological methods in the theory of nonlinear integral equations. Pergamon Press, 1964. Zbl0111.30303
- [25] A. Manes and A.M. Micheletti, Un'estensione della teoria variazionale classica degli autovalori per operatori ellittici del secondo ordine. Boll. U. M. I., t. 7, 1973, p. 285-301. Zbl0275.49042MR344663
- [26] A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications. J. Funct. Analysis, t. 14, 1973, p. 349-381. Zbl0273.49063MR370183
Citations in EuDML Documents
top- Q. Choi, Sungki Chun, Tacksun Jung, The multiplicity of solutions and geometry of a nonlinear elliptic equation
- Flavio Donati, A note on the solvability of nonlinear elliptic problems with jumping nonlinearities
- Martin Schechter, A generalization of the saddle point method with applications
- Antonio Marino, Claudio Saccon, Some variational theorems of mixed type and elliptic problems with jumping nonlinearities
- M. Arias, J. Campos, M. Cuesta, J.-P. Gossez, Asymmetric elliptic problems with indefinite weights
- Pavel Drábek, Landesman-Lazer type condition and nonlinearities with linear growth
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