Existence and concentration of positive solutions for Schrödinger-Poisson systems with steep well potential

Chen, Sitong; Tang, Xianhua; Peng, Jiawu

doi:10.1556/012.2018.55.1.1388

Cited by 2 publications

(1 citation statement)

References 72 publications

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“…In [25], Shen and Yao obtained the existence of positive ground state solutions and concentration results for (1.2) via some new analytical skills and Nehari-Pohožaev identity. In [24], Shen concerned with the nontrivial solutions for fractional Schrödinger-Poisson system with the Bessel operator.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$

Zheng

2021

Taiwanese J. Math.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$

Zheng

2021

Taiwanese J. Math.

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Ground state sign-changing solution for Schrödinger-Poisson system with steep potential well

Kang

Liu

Tang

2023

DCDS-B

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In the present paper, we investigate a class of nonlinear Schrödinger-Poisson system<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} -\Delta u+V_\lambda(x)u+\mu \phi u = f(u) \quad \quad \ {\rm{in}} \ {\mathbb{R}}^{3},\\ -\Delta \phi = u^2 \quad \quad \quad \quad \ \ \quad \quad \quad \quad \quad \quad {\rm{in}} \ {\mathbb{R}}^{3}, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula>where <inline-formula><tex-math id="M1">\begin{document}$ \mu>0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ V_\lambda(x) = \lambda V(x)+1 $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M3">\begin{document}$ \lambda>0 $\end{document}</tex-math></inline-formula>. Under some mild assumptions on <inline-formula><tex-math id="M4">\begin{document}$ V $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ f $\end{document}</tex-math></inline-formula>, we prove the existence of ground state sign-changing solution for <inline-formula><tex-math id="M6">\begin{document}$ \lambda>0 $\end{document}</tex-math></inline-formula> large enough by adopting the deformation lemma and constrained minimization arguments. Then, the least energy of sign-changing solutions is strictly large than two times the ground state energy. Additionally, the phenomenon of concentration for ground state sign-changing solutions is also analysed as <inline-formula><tex-math id="M7">\begin{document}$ \lambda\rightarrow \infty $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M8">\begin{document}$ \mu\rightarrow0 $\end{document}</tex-math></inline-formula>.

show abstract

Existence and concentration of positive solutions for Schrödinger-Poisson systems with steep well potential

Cited by 2 publications

References 72 publications

Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$

Solutions of Perturbed Fractional Schrödinger–Poisson System with Critical Nonlinearity in $\mathbb{R}^{3}$

Ground state sign-changing solution for Schrödinger-Poisson system with steep potential well

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