Elliptic equations involving multi-singular potentials and critical nonlinearity

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Let Ω be a smooth open-bounded domain in RN(N ⩾ 5). We deal with the multi-singular critical elliptic problem (1.1) where µk ∈ R, 2∗ := 2N/(N-4), ωk ∈ Ω (1 ⩽ k ⩽ m) and G(x) is a bounded positive function on Ω¯. By exploiting the impact of the coefficient of the critical nonlinearity, we, by making use of variational method, establish the existence of a positive solution to problem (1.1).