2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126487We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory, we obtain a multiplicity result for a class of semilinear elliptic equations.Analysis of PDEs35J60text