Semilinear elliptic problems with asymmetric nonlinearities

In this paper we are concerned on the semilinear elliptic problem { − Δ u = − λ | u | q − 2 u + a u + b ( u + ) p − 1 in Ω , u = 0 , on ∂ Ω , where Ω ⊆ R N is a bounded domain with regular boundary ∂ Ω , 1 < q < 2 < p ≤ 2 ∗ . If a is between two eigenvalues, we get the existence of three nontrivial solutions for the problem above.