Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system

Zhang, Qiongfen; Chen, Kai; Li, Shuqin; Fan, Jinmei

doi:10.3934/math.2021455

AIMS Mathematics

2021

DOI: 10.3934/math.2021455

|View full text |Cite

Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system

Qiongfen Zhang¹,

Kai Chen²,

Shuqin Li

et al.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

On Schrödinger-Poisson equations with a critical nonlocal term

Zhang,

Zhang

2024

MATH

View full text Add to dashboard Cite

<abstract>In this paper, we study the following non-autonomous Schrödinger-Poisson equation with a critical nonlocal term and a critical nonlinearity: <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{\begin{aligned} & -\Delta u +V(x) u + \lambda \phi |u|^3 u = f(u) + (u^+)^5,\ \ {\rm in } \ \ \ \ \mathbb{R}^3,\\ & -\Delta \phi = |u|^5, \ \ {\rm in } \ \ \ \ \mathbb{R}^3. \end{aligned}\right. \end{equation*} $\end{document} </tex-math></disp-formula> First, we consider the case that the nonlinearity satisfies the Berestycki-Lions type condition with critical growth. Second, we consider the case that $ \mathrm{int}V^{-1}(0) $ is contained in a spherical shell. By using variational methods, we obtain the existence and asymptotic behavior of positive solutions.</abstract>

show abstract

On Schrödinger-Poisson equations with a critical nonlocal term

Zhang,

Zhang

2024

MATH

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Existence of axially symmetric solutions for a kind of planar Schrödinger-Poisson system

Cited by 1 publication

References 24 publications

On Schrödinger-Poisson equations with a critical nonlocal term

On Schrödinger-Poisson equations with a critical nonlocal term

Contact Info

Product

Resources

About