Symmetry of positive solutions to biharmonic Lane-Emden equation with singular set

In this paper, we are devoted to studying the positive weak, punctured or distributional solutions to the biharmonic Lane-Emden equation {equation*} Δ² u=uᵖ in \ RN Z, {equation*} where N≥5, 1<p+4/N-4, and the singular set Z represents a closed and proper subset of x₁=0. The symmetry and monotonicity properties of the singular solutions will be given by taking advantage of the moving plane method and the approach of moving spheres.