Uniqueness of asymptotic limit of ground states for a class of quasilinear Schrödinger equation with H1-critical growth in ℝ3. Issue 2 (22nd January 2022)

• Record Type: Journal Article
• Authors: Adachi, Shinji; Shibata, Masataka; Watanabe, Tatsuya
• Is Part Of: Applicable analysis. Volume 101:Issue 2(2022)
• Page Start: 671
• Page End: 691
• Publication Date: 2022-01-22
• Subjects: Quasilinear elliptic equation -- asymptotic behavior -- variational method; 35J62 -- 35J20 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1757079
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We are interested in the asymptotic behavior of ground states for a class of quasilinear elliptic equations in R 3 when the nonlinear term has H 1 -critical growth. In the previous result [Adachi et al. Asymptotic property of ground states for a class of quasilinear Schrödinger equation with H 1 -critical growth. Calc Var Partial Differential Equations. 2019;58(3). Art. 88, 29 pp.], it was shown that, after a suitable scaling, the ground state converges to the Talenti function. However, the uniqueness of the limit of the full sequence was not obtained, which was essentially owning to the fact that the Talenti function does not belong to L 2 ( R 3 ) . In this paper, by constructing a refined test function and performing a detailed asymptotic analysis, we are able to obtain the uniqueness of asymptotic limit of ground states.