Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces

Juan Carlos Fernández, Jimmy Petean, Oscar Palmas

Given an isoparametric function $f$ on the $n$-dimensional round sphere, we consider functions of the form $u=w\circ f$ to reduce the semilinear elliptic problem \[ -Δ_{g_0}u+λu=λ…