Existence and nonexistence of positive solutions for a static Schrodinger-Poisson-Slater equation | |
Liu, Zhisu1; Zhang, Zhitao2,3; Huang, Shuibo4 | |
2019-04-15 | |
Source Publication | JOURNAL OF DIFFERENTIAL EQUATIONS |
ISSN | 0022-0396 |
Volume | 266Issue:9Pages:5912-5941 |
Abstract | In this paper we study the following type of the Schrodinger-Poisson-Slater equation with critical growth -Delta u + (u(2) * 1/vertical bar 4 pi x vertical bar)u = mu vertical bar u vertical bar(p-1)u + vertical bar u vertical bar(4)u, in R-3, where mu > 0 and p is an element of (11/7, 5). For the case of p is an element of (2, 5). We develop a novel perturbation approach, together with the well-known Mountion-Pass theorem, to prove the existence of positive ground states. For the case of p = 2, we obtain the nonexistence of nontrivial solutions by restricting the range of mu and also study the existence of positive solutions by the constrained minimization method. For the case of p is an element of (11/7, 2), we use a truncation technique developed by Brezis and Oswald [9] together with a measure representation concentration-compactness principle due to Lions [27] to prove the existence of radial symmetrical positive solutions for mu is an element of (0, mu*) with some mu* > 0. The above results nontrivially extend some theorems on the subcritical case obtained by Ianni and Ruiz [18] to the critical case. (C) 2018 Elsevier Inc. All rights reserved. |
Keyword | Schrodinger-Poisson-Slater problem Positive solution Perturbation technique Concentration-compactness principle |
DOI | 10.1016/j.jde.2018.10.048 |
Language | 英语 |
Funding Project | NSF of China[11701267] ; NSF of China[11761059] ; NSF of China[11771428] ; NSF of Hunan Province[2017JJ3265] ; Fundamental Research Funds for the Central Universities[31920170001] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000458515200023 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/32473 |
Collection | 数学所 |
Corresponding Author | Zhang, Zhitao |
Affiliation | 1.Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Northwest Minzu Univ, Sch Math & Comp, Lanzhou 730000, Gansu, Peoples R China |
Recommended Citation GB/T 7714 | Liu, Zhisu,Zhang, Zhitao,Huang, Shuibo. Existence and nonexistence of positive solutions for a static Schrodinger-Poisson-Slater equation[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2019,266(9):5912-5941. |
APA | Liu, Zhisu,Zhang, Zhitao,&Huang, Shuibo.(2019).Existence and nonexistence of positive solutions for a static Schrodinger-Poisson-Slater equation.JOURNAL OF DIFFERENTIAL EQUATIONS,266(9),5912-5941. |
MLA | Liu, Zhisu,et al."Existence and nonexistence of positive solutions for a static Schrodinger-Poisson-Slater equation".JOURNAL OF DIFFERENTIAL EQUATIONS 266.9(2019):5912-5941. |
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