In this paper we present a unified approach to investigate existence and concentration of positive solutions for the following class of quasilinear Schrödinger equations,

where \(N\geqslant3, \varepsilon > 0, V(x)\) is a positive external potential,h is a real function with subcritical or critical growth. The problem is quite sensitive to the sign changing of the quasilinear term as well as to the presence of the parameter \(\gamma>0\). Nevertheless, by means of perturbation type techniques, we establish the existence of a positive solution \(u_{\varepsilon,\gamma}\) concentrating, as \(\varepsilon\rightarrow 0\), around minima points of the potential.

在本文中，我们提供了一种统一的方法来研究以下一类拟线性Schrödinger方程的正解的存在性和集中性，

其中\（N \ geqslant3，\ varepsilon> 0，V（x）\）是一个正外部势能，h是具有次临界或临界增长的实函数。该问题对于准线性项的符号变化以及参数\（\ gamma> 0 \）的存在非常敏感。但是，通过摄动类型的技术，我们建立了一个正解\（u _ {\ varepsilon，\ gamma} \）的存在，该正解集中为\（\ varepsilon \ rightarrow 0 \），围绕着势的极小点。