On nonlinear Schr\"{o}dinger equations on the hyperbolic space

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

doi:10.1016/j.jmaa.2020.124516

On nonlinear Schr\"{o}dinger equations on the hyperbolic space

Analysis of PDEs 2020-09-04 v1

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

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Abstract

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.

Keywords

nonlinear schrödinger equation weak solutions nonlinear schrödinger equations

Cite

@article{arxiv.2009.01602,
  title  = {On nonlinear Schr\"{o}dinger equations on the hyperbolic space},
  author = {Matija Cencelj and István Faragó and Róbert Horváth and Dušan D. Repovš},
  journal= {arXiv preprint arXiv:2009.01602},
  year   = {2020}
}

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