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Multiple positive solutions for Schrödinger-Poisson system with singularity on the Heisenberg group.
- Source :
-
Journal of Inequalities & Applications . 2/5/2024, Vol. 2024 Issue 1, p1-16. 16p. - Publication Year :
- 2024
-
Abstract
- In this work, we study the following Schrödinger-Poisson system { − Δ H u + μ ϕ u = λ u − γ , in Ω , − Δ H ϕ = u 2 , in Ω , u > 0 , in Ω , u = ϕ = 0 , on ∂ Ω , where Δ H is the Kohn-Laplacian on the first Heisenberg group H 1 , and Ω ⊂ H 1 is a smooth bounded domain, μ = ± 1 , 0 < γ < 1 , and λ > 0 are some real parameters. For the above system, we prove the existence and uniqueness of positive solution for μ = 1 and each λ > 0 . Multiple solutions of the system are also considered for μ = − 1 and λ > 0 small enough using the critical point theory for nonsmooth functional. [ABSTRACT FROM AUTHOR]
- Subjects :
- *POISSON'S equation
Subjects
Details
- Language :
- English
- ISSN :
- 10255834
- Volume :
- 2024
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Inequalities & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 175253879
- Full Text :
- https://doi.org/10.1186/s13660-024-03096-3