Semilinear elliptic problems with asymmetric nonlinearities

In this paper we are concerned on the semilinear elliptic problem {−Δu=−λ|u|q−2u+au+b(u+)p−1inΩ,u=0,on∂Ω, where Ω⊆RN is a bounded domain with regular boundary ∂Ω, 1