On singular elliptic equations involving oscillatory terms

We guarantee the existence of infinitely many distinct non-negative solutions of the elliptic problem { − div ( | x | − 2 a ∇ u ) = | x | − 2 b f ( u ) in Ω , u = 0 on ∂ Ω , where Ω is a bounded open domain in R n ( n ≥ 3 ) containing the origin, a , b are positive numbers of a certain range, and f is a continuous function oscillating either at the origin or at infinity. The sequence of solutions in L ∞ -norm tends to 0 (resp., to + ∞ ) whenever f oscillates at the origin (resp., at infinity).