We prove 1-dimensional symmetry of positive eigenfunctions of the p-Laplacian in Euclidean space \(\mathbb {R}^n\) which are comparable to certain positive eigenfunctions and also prove radial symmetry of positive solutions to Euler–Lagrange equations arising from Hardy’s inequality with two radial weights in the punctured space \(\mathbb {R}^n \setminus \{0\}\) , which are comparable to certain positive radial solutions of the equation. As an application we also establish sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear p-Laplace equations in Euclidean space.
