Artículos de revistas
Two solutions for a singular elliptic equation by variational methods
Registro en:
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. Scuola Normale Superiore, v. 11, n. 1, n. 143, n. 165, 2012.
0391-173X
WOS:000303851100004
Autor
Montenegro, M
Silva, EAB
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) We find two nontrivial solutions of the equation -Delta u = (- 1/u(beta) + lambda u(p)) chi({u > 0}) in Omega with Dirichlet boundary condition, where 0 < beta < 1 and 0 < p < 1. In the first approach we consider a sequence of epsilon-problems with 1/u(beta) replaced by u(q)/(u + epsilon)(q-beta) with 0 < q < p < 1. When the parameter lambda > 0 is large enough, we find two critical points of the corresponding epsilon-functional which, at the limit as epsilon -> 0, give rise to two distinct nonnegative solutions of the original problem. Another approach is based on perturbations of the domain Omega, we then find a unique positive solution for lambda large enough. We derive gradient estimates to guarantee convergence of approximate solutions u(epsilon) to a true solution u of the problem. 11 1 143 165 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)