In this paper, we study the following Schrödinger-Poisson system with critical growth: \begin{equation*} \begin{cases}-\Delta u+V(x)u+ \phi(x)u =f(u)+|u|^4u, \ & x\in\mathbb{R}^3, \\ -\Delta \phi=u^2, \ & x\in\mathbb{R}^3. \end{cases} \end{equation*} We establish the existence of a positive ground state solution and a least energy sign-changing solution, providing that the nonlinearity $f$ is super-cubic, subcritical and that the potential $V(x)$ has a potential well.
Yinbin Deng
,
Wei Shuai
,
Xiaolong Yang
. SIGN-CHANGING SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER-POISSON SYSTEM WITH CRITICAL GROWTH*[J]. Acta mathematica scientia, Series B, 2023
, 43(5)
: 2291
-2308
.
DOI: 10.1007/s10473-023-0521-9
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