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.

@article{ASNSP_2010_5_9_2_423_0, author = {Wei, Juncheng and Yan, Shusen}, title = {On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {2}, year = {2010}, pages = {423-457}, zbl = {1204.35094}, mrnumber = {2731162}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2010_5_9_2_423_0} }

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, Serie 5, Volume 9 (2010) no. 2, pp. 423-457. http://www.numdam.org/item/ASNSP_2010_5_9_2_423_0/

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