On nonlinear Schrödinger equations on the hyperbolic space

Cencelj, Matija (author), Faragó, István (author), Horváth, Róbert (author), Repovš, Dušan (author)

We study existence of weak solutions for certain classes of nonlinear Schrödinger equations on the Poincaré ball model ▫$\mathbb{B}^N$▫, ▫$N\ge 3$▫. By using the Palais principle of symmetric criticality and suitable group theoretical arguments, we establish the existence of a nontrivial (weak) solution.

• Language: English
• Keywords: Schrödinger equation, Poincaré ball model, Palais principle, Laplace-Beltrami operator, Hadamard manifold, Kirchhoff-type problem
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2020
• Number of pages: art. 124516 (12 str.)
• Numbering: Vol. 492, iss.2
• PID: 20.500.12556/RUL-119296
• UDC: 517.956:515.16
• ISSN on article: 0022-247X
• DOI: 10.1016/j.jmaa.2020.124516
• COBISS.SI-ID: 25766659
• Publication date in RUL: 07.09.2020