In this article, we study the generalized quasilinear Schrödinger equation $$ - \text{div}({\varepsilon ^2}{g^2}(u)\nabla u) + {\varepsilon ^2}g(u)g'(u){\left| {\nabla u} \right|^2} + V(x)u = K(x){\left| u \right|^{p - 2}}u,\;\;\;\;x \in {\mathbb{R}^N},$$ where N ≥ 3, ε> 0, 4 < p < 22*, g ϵ C 1 (ℝ, ℝ + ), V ϵ C (ℝ N ) ∩ L ∞ (ℝ N ) has a positive global minimum, and K ϵ C (ℝ N ) ∩ L ∞ (ℝ N ) has a positive global maximum. By using a change of variable, we obtain the existence and concentration behavior of ground state solutions for this problem and establish a phenomenon of exponential decay.

中文翻译：

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ℝN 中一类广义拟线性薛定谔方程基态解的存在性和集中性

在本文中，我们研究广义拟线性薛定谔方程 $$ - \text{div}({\varepsilon ^2}{g^2}(u)\nabla u) + {\varepsilon ^2}g(u)g '(u){\left| {\nabla u} \right|^2} + V(x)u = K(x){\left| u \right|^{p - 2}}u,\;\;\;\;x \in {\mathbb{R}^N},$$ 其中 N ≥ 3, ε> 0, 4 < p < 22 *, g ϵ C 1 (ℝ, ℝ + ), V ϵ C (ℝ N ) ∩ L ∞ (ℝ N ) 有一个正的全局最小值，K ϵ C (ℝ N ) ∩ L ∞ (ℝ N ) 有一个正全局最大值。通过使用变量的变化，我们获得了该问题基态解的存在性和集中性，并建立了指数衰减现象。