We find two nontrivial solutions of the equation in with Dirichlet boundary condition, where and . In the first approach we consider a sequence of -problems with replaced by with . When the parameter is large enough, we find two critical points of the corresponding -functional which, at the limit as , give rise to two distinct nonnegative solutions of the original problem. Another approach is based on perturbations of the domain , we then find a unique positive solution for large enough. We derive gradient estimates to guarantee convergence of approximate solutions to a true solution of the problem.
@article{ASNSP_2012_5_11_1_143_0, author = {Montenegro, Marcelo and Silva, Elves A. B.}, title = {Two solutions for a singular elliptic equation~by variational methods}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {143--165}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {1}, year = {2012}, mrnumber = {2953046}, zbl = {1241.35103}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_1_143_0/} }
TY - JOUR AU - Montenegro, Marcelo AU - Silva, Elves A. B. TI - Two solutions for a singular elliptic equation by variational methods JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 143 EP - 165 VL - 11 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_1_143_0/ LA - en ID - ASNSP_2012_5_11_1_143_0 ER -
%0 Journal Article %A Montenegro, Marcelo %A Silva, Elves A. B. %T Two solutions for a singular elliptic equation by variational methods %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 143-165 %V 11 %N 1 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_1_143_0/ %G en %F ASNSP_2012_5_11_1_143_0
Montenegro, Marcelo; Silva, Elves A. B. Two solutions for a singular elliptic equation by variational methods. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 1, pp. 143-165. http://archive.numdam.org/item/ASNSP_2012_5_11_1_143_0/
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