Some remarks on the number of solutions of some nonlinear elliptic problems
Annales de l'I.H.P. Analyse non linéaire, Volume 2 (1985) no. 2, p. 143-156
@article{AIHPC_1985__2_2_143_0,
     author = {Solimini, Sergio},
     title = {Some remarks on the number of solutions of some nonlinear elliptic problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {2},
     number = {2},
     year = {1985},
     pages = {143-156},
     zbl = {0583.35044},
     mrnumber = {794004},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1985__2_2_143_0}
}
Solimini, Sergio. Some remarks on the number of solutions of some nonlinear elliptic problems. Annales de l'I.H.P. Analyse non linéaire, Volume 2 (1985) no. 2, pp. 143-156. http://www.numdam.org/item/AIHPC_1985__2_2_143_0/

[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. | MR 320844 | Zbl 0288.35020

[2] M. Berger and E. Podolac, On the solutions of a nonlinear Dirichlet Problem. Indiana Univ. Math. J., t. 24, 1975, p. 837-846. | MR 377274 | Zbl 0329.35026

[3] S. Fucik, Remarks on a result by A. AMBROSETTI and G. PRODI. Boll. U. M. I., t. 11, 1975, p. 259-267. | MR 382849 | Zbl 0303.35037

[4] H. Berestycki, Le nombre de solutions de certains problèmes semilinéaires elliptiques. J. Funct. An., t. 40, 1981, p. 1-29. | MR 607588 | Zbl 0452.35038

[5] J.L. Kazdan and F.W. Warner, Remarks on some quasilinear elliptic equations. Comm. Pure. Appl. Math., t. 28, 1975, p. 567-597. | MR 477445 | Zbl 0325.35038

[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. | MR 524624 | Zbl 0394.35040

[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. | MR 549877 | Zbl 0416.35029

[8] D.G. De Figueiredo, On the superlinear Ambrosetti-Prodi problems. Nonlin. An. TMA, t. 8, 1984, p. 655-665. | MR 746723 | Zbl 0554.35045

[9] D.G. De Figueiredo and S. Solimini, A variational approach to superlinear elliptic problems. Comm. PDE, t. 9, 1984, p. 699. | MR 745022 | Zbl 0552.35030

[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. | MR 639539 | Zbl 0496.35039

[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. | MR 709044 | Zbl 0522.35045

[12] A. Ambrosetti, Elliptic equations with jumping nonlinearities. J. Math. Phys. Sci. (to appear). | MR 755462 | Zbl 0589.35043

[13] H. Hofer, Variational and topological methods in partially ordered Hilbert spaces. Math. Annalen, t. 261, 1982, p. 493-514. | MR 682663 | Zbl 0488.47034

[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). | MR 787722 | Zbl 0584.35053

[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. | Zbl 0533.35037

[16] E. Podolak, On the range operator equations with an asymptotically nonlinear term. Indiana Univ. Math. J., t. 25, 1976, p. 1127-1137. | MR 425698 | Zbl 0353.47035

[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. | Numdam | Zbl 0495.35001

[18] B. Ruf, On nonlinear elliptic problems with jumping nonlinearities. Ann. Mat. Pure e Appl. Serie IV, t. CXXVIII, 1981, p. 133-151. | MR 640779 | Zbl 0475.35046

[19] Adimurthi and P.N. Srikanth, On the exact number of solutions at infinity for Ambrosetti-Prodi class of problems, preprint.

[20] S. Solimini, Multiplicity results for a nonlinear Dirichlet problem. Proc. Royal Soc. Edinburgh, t. 96 A, 1984. | MR 760781 | Zbl 0557.35052

[21] A.C. Lazer and P.J. Mckenna, Multiplicity results for a semi-linear boundary value problem with the nonlinearity crossing higher eigenvalues, preprint. | MR 1237124

[22] D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, 1980. | MR 567696 | Zbl 0457.35001

[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. | MR 499709 | Zbl 0351.35037

[24] M.A. Krasnosel'Skii, Topological methods in the theory of nonlinear integral equations. Pergamon Press, 1964. | Zbl 0111.30303

[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. | MR 344663 | Zbl 0275.49042

[26] A. Ambrosetti and P. Rabinowitz, Dual variational methods in critical point theory and applications. J. Funct. Analysis, t. 14, 1973, p. 349-381. | MR 370183 | Zbl 0273.49063