Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 5 (1978) no. 1, p. 15-28 
@article{ASNSP_1978_4_5_1_15_0,
     author = {Ambrosetti, Antonio and Mancini, Giovanni},
     title = {Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 5},
     number = {1},
     year = {1978},
     pages = {15-28},
     zbl = {0375.35024},
     mrnumber = {487001},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1978_4_5_1_15_0}
}

Ambrosetti, Antonio; Mancini, Giovanni. Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 5 (1978) no. 1, pp. 15-28. http://www.numdam.org/item/ASNSP_1978_4_5_1_15_0/

[1] A. Ambrosetti - G. Mancini, Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance, to appear on J. Diff. Eq.

[2] P.H. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, to appear. | MR 501092 | Zbl 0466.58015

[3] S Fučik - M. Krbeč, Boundary value problems with bounded nonlinearity and general null space of the linear part, to appear on Math. Z. | MR 473513 | Zbl 0337.35034

[4] P. Hess, A remark on a preceding paper of Fučik and Krbeč, to appear on Math. Z. | MR 473514 | Zbl 0356.35030

[5] J.T. Schwartz, Nonlinear functional analysis, Gordon and Breach Intersc. Publ. (1969). | MR 433481 | Zbl 0203.14501

[6] S. Ahmad - A.C. Lazer - J.L. Paul, Elementary critical point theory and perturbation of elliptic boundary value problems at resonance, Indiana Univ. Math. J., 25 (1976), pp. 933-944. | MR 427825 | Zbl 0351.35036

[7] A. Ambrosetti, On the existence of multiple solutions for a class of nonlinear boundary value problems, Rend. Sem. Mat. Univ. Padova, 49 (1973), pp. 195-204. | Numdam | MR 336068 | Zbl 0273.35037

[8] E.N. Dancer, On a nonlinear elliptic boundary value problem, Bull. Australian Math. Soc., 12 (1975), pp. 399-405. | MR 385318 | Zbl 0297.35031