Abstract
We study the following critical Schrödinger-Possion system with steep potential well
where \(\lambda >0\) is a positive parameter, \(V:{\mathbb {R}}^{3}\rightarrow {\mathbb {R}}\) is a continuous function and f is a continuous subcritical nonlinearity. Under some certain assumptions on V and f, for any \(\lambda \ge \lambda _0>0\), we prove the existence of a ground state solution via variational methods. Moreover, the concentration behavior of the ground state solution is also described as \(\lambda \rightarrow \infty \). Our results extends that in Jiang[11](J. Differ. Equ. 2011) and Zhao[21](J. Differ. Equ. 2013) to the critical growth case.
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Communicated by K Sandeep.
Supported by the NSFC (12171014, ZR2020MA005, ZR2021MA096).
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Mo, X., Li, M. & Mao, A. Ground state solutions to critical Schrödinger–Possion system with steep potential well. Indian J Pure Appl Math (2024). https://doi.org/10.1007/s13226-024-00580-w
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DOI: https://doi.org/10.1007/s13226-024-00580-w