We are interested in studying the existence of solution for the generalized quasilinear Schrödinger equation: (P) $\begin{array}{l}-\mathrm{d}\mathrm{i}\mathrm{v}\left(g^2\right(u\left)\mathrm{\nabla }u\right)+g\left(u\right)g^{\prime }\left(u\right)|\mathrm{\nabla }u{|}^2+V\left(x\right)u=h(x,u),\\ u\in H^1\left({\mathbb{R}}^N\right)\end{array}$(P) in ${\mathbb{R}}^N$, where $N\ge 3$, g and h are suitable smooth functions and V is a potential that may change sign and be unbounded. By using a change of variables and variational arguments, we obtain the existence of a nontrivial solution for the given problem.

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具有符号变化无界势的广义拟线性方程

我们有兴趣研究广义拟线性薛定谔方程解的存在性：(P)$\begin{array}{l}-\mathrm{d}\mathrm{一世}\mathrm{v}\left(G^2\right(你\left)\mathrm{\nabla }你\right)+G\left(你\right)G^{\text{'}}\left(你\right)|\mathrm{\nabla }你{|}^2+五\left(X\right)你=H(X,你),\\ 你\in H^1\left({\mathbb{R}}^{ñ}\right)\end{array}$(P)在${\mathbb{R}}^{ñ}$， 在哪里$ñ\ge 3$, g和h是合适的平滑函数，V是可能改变符号且无界的势。通过使用变量和变分参数的变化，我们获得给定问题的非平凡解的存在性。