We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We show that a class of semilinear Laplace–Beltrami equations on the unit sphere in 
${{\mathbb{R}}^{n}}$ has infinitely many rotationally symmetric solutions. The solutions to these equations are the solutions to a two point boundary value problem for a singular ordinary differential equation. We prove the existence of such solutions using energy and phase plane analysis. We derive a Pohozaev-type identity in order to prove that the energy to an associated initial value problem tends to infinity as the energy at the singularity tends to infinity. The nonlinearity is allowed to grow as fast as 
${{\left| s \right|}^{p-1}}s$ for 
$\left| s \right|$ large with 
$1\,<\,p\,<\,\left( n+5 \right)/\left( n-3 \right)$.
