Asymptotic properties of standing waves for Maxwell-Schrodinger-Poisson system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Hu, Tingxi¹  Lu, Lu² 

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] Zhongnan Univ Econ & Law, Sch Stat & Math, Wuhan 430073, Peoples R China

关键词: Maxwell-Schrodinger-Poisson system;    Asymptotic behavior;    Blow up;   

DOI  :  10.1016/j.jmaa.2019.123835

来源: Elsevier

【 摘 要 】

In this paper, we study the asymptotic properties of minimizers for a class of constraint minimization problems derived from the Maxwell-Schrodinger-Poisson system -Delta u - (vertical bar u vertical bar(2) * vertical bar x vertical bar(-1))u - alpha vertical bar u vertical bar(2p)u - mu(p)u = 0, x is an element of R-3 on the L-2-spheres A(lambda)= {u is an element of H-1(R-3) : integral(R3) vertical bar u vertical bar(2)dx = lambda}, where alpha,p > 0. Let lambda* = parallel to Q(2/3)parallel to(2)(2), and Q(2/3) is the unique (up to translations) positive radial solution of -3p/2 Delta u + 2-p/2u - vertical bar u vertical bar(2p)u = 0 in R-3 with p = 2/3. We prove that if lambda < alpha (-3/2)lambda*, then minimizers are relatively compact in A(lambda) as p NE arrow 2/3. On the contrary, if lambda > alpha (-3/2)lambda*, by directly using asymptotic analysis, we prove that all minimizers must blow up and give the detailed asymptotic behavior of minimizers. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free