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 (Formula presented.) where N≥5, 1<p≤N+4N-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.