On nonlinear Schrödinger equations on the hyperbolic space

Matija Cencelj, István Faragó, Róbert Horváth, Dušan D. Repovš

Published 2020-09-03Version 1

We study existence of weak solutions for certain classes of nonlinear Schr\"{o}dinger equations on the Poincar\'{e} ball model $\mathbb{B}^N$, $N\geq 3$. By using the Palais principle of symmetric criticality and suitable group theoretical arguments, we establish the existence of a nontrivial (weak) solution.