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

摘要

We study a class of singular elliptic equations involving critical Sobolev exponent and Kirchhoff-type nonlocal term ? a + b R ? |?u| 2dx_x005f ?u = u 5 + g(x, u) + λu ?γ , x ∈ ?, u > 0, x ∈ ?, u = 0, x ∈ ??, where ? ? R3 is a bounded domain, a, b, λ > 0, 0 < γ < 1 and g ∈ C(? × R) satisfies some conditions. By the perturbation method, variational method and some analysis techniques, we establish a multiplicity theorem.