On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 423-457.

We consider an elliptic problem of Ambrosetti-Prodi type involving critical Sobolev exponent on a bounded smooth domain. We show that if the domain has some symmetry, the problem has infinitely many (distinct) solutions whose energy approach to infinity even for a fixed parameter, thereby obtaining a stronger result than the Lazer-McKenna conjecture.

Classification : 35J65, 35B38, 47H15
Wei, Juncheng 1 ; Yan, Shusen 2

1 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
2 Department of Mathematics, The University of New England, Armidale, NSW 2351, Australia
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     title = {On a stronger {Lazer-McKenna} conjecture for {Ambrosetti-Prodi} type problems},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Wei, Juncheng; Yan, Shusen. On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 423-457. http://archive.numdam.org/item/ASNSP_2010_5_9_2_423_0/

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