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- Title
A note on the Nonlinear Schrödinger Equation on Cartan-Hadamard manifolds with unbounded and vanishing potentials.
- Authors
Appolloni, Luigi; Bisci, Giovanni Molica; Secchi, Simone
- Abstract
We study the semilinear equation-Δgu+V(σ)u = f(u) on a Cartan-Hadamard manifold Μ of dimension N ≥ 3, and we prove the existence of a nontrivial solution under suitable assumptions on the potential function V ε C(Μ). In particular, the decay of V at infinity is allowed, with some restrictions related to the geometry of Μ. We generalize some results proved in RN by Alves et al.
- Subjects
NONLINEAR Schrodinger equation; SEMILINEAR elliptic equations
- Publication
Mathematical Methods in the Applied Sciences, 2024, Vol 47, Issue 7, p5549
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9878