We consider the system -△u = λf(u,v); x ∈Ω -Δf = λg(u,v); x ∈Ω u = 0 = u;x ∈aΩ, where Q is a ball in RN, JV > 1 and 90 is its boundary, A is a positive parameter, and / and g are smooth functions that are negative at the origin (semipositone system) and satisfy certain linear growth conditions at infinity. We establish nonexistence of positive solutions when A is large. Our proofs depend on energy analysis and comparison methods.
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