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Li, Shiqi; Song, Yueqiang
Open Mathematics, 09/2023, Letnik: 21, Številka: 1Journal Article
We deal with multiplicity of solutions to the following Schrödinger-Poisson-type system in this article: where is the Kohn-Laplacian and is a smooth bounded region on the first Heisenberg group , , and are some real parameters, and , satisfying natural growth conditions. By the limit index theory and the concentration compactness principles, we prove that the aforementioned system has multiplicity of solutions for , where is the best Sobolev constant. The novelties of this article are the presence of critical nonlinear term, and the system is set on the Heisenberg group.
