Multiplicity of solutions for a class of critical Schrodinger-Poisson systems on the Heisenberg group

被引:1
作者
Li, Shiqi [1 ]
Song, Yueqiang [1 ]
机构
[1] Changchun Normal Univ, Coll Math, Changchun 130032, Peoples R China
关键词
Schrodinger-Poisson-type system; Heisenberg group; limit index; variational methods; concentration compactness principles; ASYMPTOTIC-BEHAVIOR; HARNACK INEQUALITY; EXISTENCE; UNIQUENESS; PRINCIPLE; EQUATIONS;
D O I
10.1515/math-2023-0113
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We deal with multiplicity of solutions to the following Schrodinger-Poisson-type system in this article: {Delta(H)u -mu(1)phi(1)u = |u(2)|u + F-u(xi, u, nu) in Omega, -Delta(H)nu + mu(2) phi(2)nu = |nu|(2)nu + F-nu(xi, u, nu) in Omega, -Delta(H)phi(1) = u(2) , -Delta(H) phi(2) =nu(2) in Omega, phi(1) = phi(2) = u = nu = 0 , in Omega, where Delta(H) is the Kohn-Laplacian and Omega is a smooth bounded region on the first Heisenberg group H-1, mu(1), and mu(2) are some real parameters, and F= (x, u, v) F-u =partial derivative F/partial derivative u, F-v = partial derivative F/partial derivative u 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 mu(1), mu(2) < |Omega|S-1/2 where S 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.
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页数:15
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