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Ground State Solutions for the Nonlinear Schrödinger–Bopp–Podolsky System with Critical Sobolev Exponent
Advanced Nonlinear Studies ( IF 2.1 ) Pub Date : 2020-08-01 , DOI: 10.1515/ans-2020-2097 Lin Li 1 , Patrizia Pucci 2 , Xianhua Tang 3
Advanced Nonlinear Studies ( IF 2.1 ) Pub Date : 2020-08-01 , DOI: 10.1515/ans-2020-2097 Lin Li 1 , Patrizia Pucci 2 , Xianhua Tang 3
Affiliation
Abstract In this paper, we study the existence of ground state solutions for the nonlinear Schrödinger–Bopp–Podolsky system with critical Sobolev exponent { - Δ u + V ( x ) u + q 2 ϕ u = μ | u | p - 1 u + | u | 4 u in ℝ 3 , - Δ ϕ + a 2 Δ 2 ϕ = 4 π u 2 in ℝ 3 , \left\{\begin{aligned} \displaystyle{}{-}\Delta u+V(x)u+q^{2}\phi u&% \displaystyle=\mu|u|^{p-1}u+|u|^{4}u&&\displaystyle\phantom{}\mbox{in }\mathbb% {R}^{3},\\ \displaystyle{-}\Delta\phi+a^{2}\Delta^{2}\phi&\displaystyle=4\pi u^{2}&&% \displaystyle\phantom{}\mbox{in }\mathbb{R}^{3},\end{aligned}\right. where μ > 0 {\mu>0} is a parameter and 2 < p < 5 {2
中文翻译：
具有临界 Sobolev 指数的非线性 Schrödinger-Bopp-Podolsky 系统的基态解
摘要 在本文中，我们研究了具有临界 Sobolev 指数 { - Δ u + V ( x ) u + q 2 ϕ u = μ | 的非线性 Schrödinger-Bopp-Podolsky 系统的基态解的存在性 你| p - 1 u + | 你| 4 u in ℝ 3 , - Δ ϕ + a 2 Δ 2 ϕ = 4 π u 2 in ℝ 3 , \left\{\begin{aligned} \Delta u+V(x)u+q^{2}\phi u&% \displaystyle=\mu|u|^{p-1}u+|u|^{4}u&&\displaystyle\phantom{}\mbox{in }\mathbb% {R}^{3},\\ \displaystyle{-}\Delta\phi+a^{2}\Delta^{2}\phi&\displaystyle=4\pi u^{2}&&% \displaystyle\phantom{}\mbox{in }\mathbb{R}^{3},\end{aligned}\right. 其中 μ > 0 {\mu>0} 是一个参数并且 2 < p < 5 {2
更新日期：2020-08-01
中文翻译：
具有临界 Sobolev 指数的非线性 Schrödinger-Bopp-Podolsky 系统的基态解
摘要 在本文中，我们研究了具有临界 Sobolev 指数 { - Δ u + V ( x ) u + q 2 ϕ u = μ | 的非线性 Schrödinger-Bopp-Podolsky 系统的基态解的存在性 你| p - 1 u + | 你| 4 u in ℝ 3 , - Δ ϕ + a 2 Δ 2 ϕ = 4 π u 2 in ℝ 3 , \left\{\begin{aligned} \Delta u+V(x)u+q^{2}\phi u&% \displaystyle=\mu|u|^{p-1}u+|u|^{4}u&&\displaystyle\phantom{}\mbox{in }\mathbb% {R}^{3},\\ \displaystyle{-}\Delta\phi+a^{2}\Delta^{2}\phi&\displaystyle=4\pi u^{2}&&% \displaystyle\phantom{}\mbox{in }\mathbb{R}^{3},\end{aligned}\right. 其中 μ > 0 {\mu>0} 是一个参数并且 2 < p < 5 {2
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