We consider the following quasilinear Schrödinger equation [Formula: see text] where [Formula: see text], [Formula: see text], and [Formula: see text] satisfies a weaker growth condition than the Ambrosetti–Rabinowitz type condition in Byeon and Wang [Standing waves with a critical frequency for nonlinear Schrödinger equations, Arch. Ration. Mech. Anal. 165(4) (2002) 295–316; Standing waves with a critical frequency for nonlinear Schrödinger equations, II, Calc. Var. 18(2) (2003) 207–219]. We obtain the existence of the localized bound state solutions concentrating at an isolated component of the local minimum of [Formula: see text] and whose amplitude goes to 0 as [Formula: see text].

中文翻译：

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拟线性薛定谔方程的具有临界频率的驻波

我们考虑以下拟线性薛定谔方程[公式：见正文]，其中[公式：见正文]、[公式：见正文]和[公式：见正文]满足比安布罗塞蒂-拉比诺维茨类型条件弱的增长条件。王 [非线性薛定谔方程的临界频率驻波，Arch。配给。机甲。肛门。165(4) (2002) 295–316；具有非线性薛定谔方程的临界频率的驻波，II，Calc。变量。18（2）（2003）207-219]。我们获得了集中在[公式：见文本]的局部最小值的孤立分量上的局部束缚态解的存在，其幅度变为0，如[公式：见文本]。