Two solutions for a singular elliptic equation by variational methods
Marcelo A. Montenegro, Elves A. B. Silva · ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2012
We find two nontrivial solutions of the equationu = (-with Dirichlet boundary condition, where 0 0 is large enough, we find two critical points of the corresponding ε-functional which, at the limit as ε → 0, 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 λ large enough.We derive gradient estimates to guarantee convergence of approximate solutions u ε to a true solution u of the problem.