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This paper is concerned with the attraction-repulsion chemotaxis system with superlinear logistic degradation,under homogeneous Neumann boundary conditions, in a ball Ω ⊂ R n (n ≥ 3), with constant parameters λ ∈ R, k > 1, µ, χ, ξ, α, β, γ, δ > 0. Blow-up phenomena in the system have been well investigated in the case λ = µ = 0, whereas the attraction-repulsion chemotaxis system with logistic degradation has been not studied. Under the condition that k > 1 is close to 1, this paper ensures a solution which blows up in L ∞ -norm and L σ -norm with some σ > 1 for some nonnegative initial data. Moreover, a lower bound of blow-up time is derived.

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