In this paper, some new existence results of elliptic equation of Kirchhoff-type with changing sign data and logarithmic source terms are proved, by using three different methods: direct variational method, Galerkin approach and sub-super solutions method. Our study is natural extensions from the previous recent works in [ 2–19 , 38 ], where the authors have already studied the existence of positive solutions for some classes of Laplacian elliptic problems by using one classical method for a certain class of elliptic equations.