LOCALIZED NODAL SOLUTIONS FOR SCHR(O)DINGER-POISSON SYSTEMS

In this paper,we study the existence of localized nodal solutions for Schr?dinger-Poisson systems with critical growth{-ε2 Δv+V(x)v+λψv=v5+μ|v|q-2v,in R3,-ε2Δψ=v2,in R3;v(x)→0,ψ(x)→ 0 as |x|→∞We establish,for small ε,the existence of a sequence of localized nodal solutions concentrating near a given...

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Bibliographic Details
Published in:数学物理学报（英文版） 2022, Vol.42 (5), p.1947-1970
Main Authors: Xing WANG, Rui HE, Xiangqing LIU
Format: Article
Language:English
Online Access:Get full text
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Summary:In this paper,we study the existence of localized nodal solutions for Schr?dinger-Poisson systems with critical growth{-ε2 Δv+V(x)v+λψv=v5+μ|v|q-2v,in R3,-ε2Δψ=v2,in R3;v(x)→0,ψ(x)→ 0 as |x|→∞We establish,for small ε,the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function via the perturbation method,and employ some new analytical skills to overcome the obstacles caused by the nonlocal termφu(x)=1/4π ∫R3 u2(y)/|x-y| dy.Our results improve and extend related ones in the literature.
ISSN:0252-9602
DOI:10.3969/j.issn.0252-9602.2022.05.013