Abstract This paper is concerned with the following planar Schrodinger-Poisson system { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , x ∈ R 2 , Δ ϕ = u 2 , x ∈ R 2 , where V ∈ C ( R 2 , [ 0 , ∞ ) ) is axially symmetric and f ∈ C ( R 2 × R , R ) is of subcritical or critical exponential growth in the sense of Trudinger-Moser. We obtain the existence of a nontrivial solution or a ground state solution of Nehari-type and infinitely many solutions to the above system under weak assumptions on V and f. Our theorems extend the results of Cingolani and Weth [Ann. Inst. H. Poincare Anal. Non Lineaire, 33 (2016) 169-197] and of Du and Weth [Nonlinearity, 30 (2017) 3492-3515] and Chen and Tang [J. Differential Equations, 268 (2020) 945-976], where f ( x , u ) has polynomial growth on u. In particular, some new tricks and approaches are introduced to overcome the double difficulties resulting from the appearance of both the convolution ϕ 2 , u ( x ) with sign-changing and unbounded logarithmic integral kernel and the critical growth nonlinearity f ( x , u ) .

中文翻译：

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具有临界指数增长的平面薛定谔-泊松系统的轴对称解

摘要 本文涉及以下平面薛定谔-泊松系统 { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , x ∈ R 2 , Δ ϕ = u 2 , x ∈ R 2 ,其中 V ∈ C ( R 2 , [ 0 , ∞ ) ) 是轴对称的， f ∈ C ( R 2 × R , R ) 是特鲁丁格-莫泽意义上的亚临界或临界指数增长。我们在 V 和 f 的弱假设下获得了上述系统的非平凡解或 Nehari 型基态解的存在性和无穷多解。我们的定理扩展了 Cingolani 和 Weth [Ann. 研究所 H.庞加莱肛门。Non Lineaire, 33 (2016) 169-197] 和 Du and Weth [Nonlinearity, 30 (2017) 3492-3515] 以及 Chen 和 Tang [J. 微分方程，268 (2020) 945-976]，其中 f ( x , u ) 在 u 上有多项式增长。特别是，