We investigate the following three-dimensional Kirchhoff-type problem
where Ω is a smooth bounded domain in R3, 0∈Ω, 0 < q < 1, 0 ≤ s < 1, 4 < p < 2*(s)=2(3-s), parameters a,b,λ > 0. We have established the existence of multiple positive solutions to the problem by using variational methods.