Concentrating ground state solutions for quasilinear Schrödinger equations with steep potential well. Issue 14 (26th October 2021)

• Record Type: Journal Article
• Authors: Jia, Huifang
• Is Part Of: Applicable analysis. Volume 100:Issue 14(2021)
• Page Start: 3065
• Page End: 3082
• Publication Date: 2021-10-26
• Subjects: S. Leonardi; Quasilinear Schrödinger equation -- asymptotically linear -- concentrating -- variational methods; 35J20 -- 35J25 -- 35J60; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1707814
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We are concerned with the following quasilinear Schrödinger equations (1) − Δ u + λ V ( x ) u + κ 2 [ Δ ( u 2 ) ] u = q ( x ) f ( u ), x ∈ R N, u ∈ H 1 ( R N ), where N ≥ 3, λ, κ > 0 are parameters, V and f are nonnegative continuous functions, q ( x ) is a positive bounded function. By using variational methods, we study the existence of positive ground state solutions to problem (1) when V, q and f satisfy some suitable conditions. Furthermore, the concentrating behavior of ground state solutions to problem (1) is proved. We mainly extend the results in Severo, Gloss and da Silva [On a class of quasilinear Schrödinger equations with superlinear or asymptotically linear terms. J Differ Equ. 2017;263:3550–3580], which considered quasilinear Schrödinger equations with positive potential function, to quasilinear Schrödinger equations with steep potential well.