A Schrödinger-Poisson system with the critical growth on the first Heisenberg group. (English) Zbl 1528.35052
J. Contemp. Math. Anal., Armen. Acad. Sci. 58, No. 3, 196-207 (2023) and Izv. Nats. Akad. Nauk Armen., Mat. 58, No. 3, 33-46 (2023).
Summary: In this paper, we study the Schrödinger-Poisson system with the critical growth on the first Heisenberg group. With the aid of the Green’s representation formula, the concentratio-compactness and the critical point theory, the existence of ground state solution.
MSC:
| 35J57 | Boundary value problems for second-order elliptic systems |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A15 | Variational methods applied to PDEs |
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