Multiple positive solutions for an elliptic problem involving a critical Sobolev exponent.

In this work, we study the multiple results of positive solutions for a class of elliptic problem involving a critical Sobolev exponent − △ u + λ V (x) u = μ f (x) u q − 1 + g (x) u 2 ∗ − 1 in R N , we prove that the problem has at least k distinct positive solutions. The methods used here are based on combining minimax methods, Nehari manifold and Ekeland's variational principle. [ABSTRACT FROM AUTHOR]