Opuscula Mathematica
Opuscula Math. 46, no. 3 (2026), 347-366

Existence of solutions for a doubly critical Schrödinger-Poisson system on the first Heisenberg group

Xueyan Ma
Shaoyun Shi
Yueqiang Song
Abstract. This work is devoted to the study of a class of Schrödinger-Poisson system with doubly critical growth on the first Heisenberg group. Utilizing the concentration-compactness principle associated with classical Sobolev space on the Heisenberg group and mountain pass theorem, we prove that the system admits multiple nontrivial solutions.
Keywords: Heisenberg group, Schrödinger-Poisson system, concentration-compactness principle, mountain pass theorem, nontrivial solutions.
Mathematics Subject Classification: 35A15, 35B33, 47G20.
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About the authors ▼
Xueyan Ma
College of Mathematics, Changchun Normal University, Changchun 130032, P.R. China
Shaoyun Shi
School of Mathematics and Statistics, Changchun University of Science and Technology, Changchun 130022, P.R. China
Yueqiang Song (corresponding author)
College of Mathematics, Changchun Normal University, Changchun 130032, P.R. China
About the article ▼
Communicated by Vicenţiu D. Rădulescu.
Received: 2026-04-05.
Revised: 2026-04-12.
Accepted: 2026-05-21.
Published online: 2026-06-08.
Cite this article as ▼
Xueyan Ma, Shaoyun Shi, Yueqiang Song, Existence of solutions for a doubly critical Schrödinger-Poisson system on the first Heisenberg group, Opuscula Math. 46, no. 3 (2026), 347-366, https://doi.org/10.7494/OpMath.202605211.
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