nonexistence results for classes of 3 × 3 elliptic systems

−δu = λf (v,w); x ∈ ω

−δv = μg(u,w); x ∈ ω

−δw = σh(u, v); x ∈ ω

u = v = w = 0; x ∈ ∂ω,

where ω is a ball in rⁿ , n > 1 and ∂ω is its boundary, λ, μ, σ are positive parameters bounded away from zero, and f , g, h are smooth functions that are negative at the origin (semipositone system) and satisfy certain linear growth conditions at infinity.weestablish nonexistence of positive solutions when two of the parameters λ, μ, σ are large. our proofs depend on energy analysis and comparison methods.