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.

^{1}; Yan, Shusen

^{2}

@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}, pages = {423--457}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {2}, year = {2010}, mrnumber = {2731162}, zbl = {1204.35094}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2010_5_9_2_423_0/} }

TY - JOUR AU - Wei, Juncheng AU - Yan, Shusen TI - On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 423 EP - 457 VL - 9 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2010_5_9_2_423_0/ LA - en ID - ASNSP_2010_5_9_2_423_0 ER -

%0 Journal Article %A Wei, Juncheng %A Yan, Shusen %T On a stronger Lazer-McKenna conjecture for Ambrosetti-Prodi type problems %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 423-457 %V 9 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2010_5_9_2_423_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2010_5_9_2_423_0/

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