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We study a class of singular elliptic equations involving critical Sobolev exponent and Kirchhoff-type nonlocal term − ( a + b ∫ Ω |∇u| 2dx ) ∆u = u5 + g(x, u) + λu−γ, x ∈ Ω, u > 0, x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω ⊂ R3 is a bounded domain, a, b, λ > 0, 0 < γ < 1 and g ∈ C(Ω×R) satisfies some conditions. By the perturbation method, variational method and some analysis techniques, we establish a multiplicity theorem.

Multiplicity of positive solutions for a class of singular elliptic equations with critical Sobolev exponent and Kirchhoff-type nonlocal term