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dc.contributor.authorLiu, Senli ( )
dc.contributor.authorChen, Haibo ( )
dc.contributor.authorFeng, Zhaosheng ( Orcid Icon 0000-0003-2782-4539 )
dc.identifier.citationLiu, S., Chen, H., & Feng, Z. (2020). Schrödinger-Poisson systems with singular potential and critical exponent. Electronic Journal of Differential Equations, 2020(130), pp. 1-17.en_US

In this article we study the Schrödinger-Poisson system

-Δu + V(|x|)u + λφu = ƒ(u), x ∈ ℝ3,
-Δφ = u2, x ∈ ℝ3

where V is a singular potential with the parameter α and the nonlinearity ƒ satisfies critical growth. By applying a generalized version of Lions-type theorem and the Nehari manifold theory, we establish the existence of the nonnegative ground state solution when λ = 0. By the perturbation method, we obtain a nontrivial solution to above system when λ ≠ 0.

dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSchrödinger-Poisson systemen_US
dc.subjectLions-type theoremen_US
dc.subjectSingular potentialen_US
dc.subjectGround state solutionen_US
dc.subjectCritical exponenten_US
dc.titleSchrödinger-Poisson systems with singular potential and critical exponenten_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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