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},
pages = {423--457},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {2},
year = {2010},
zbl = {1204.35094},
mrnumber = {2731162},
language = {en},
url = {archive.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, 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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