ABSTRACT

In this paper, we study the nonexistence of solutions to the quasilinear Schrödinger equations: (1) $\begin{array}{r}-{\mathrm{\Delta }}_{p}u+V\left(x\right)|u{|}^{p-2}u-{\mathrm{\Delta }}_p\left(|u{|}^{2\alpha }\right)|u{|}^{2\alpha -2}u=g(x,u),x\in {\mathbb{R}}^N,\end{array}$(1) where p-Laplacian operator ${\mathrm{\Delta }}_{p}u=\mathrm{d}\mathrm{i}\mathrm{v}\left(|\mathrm{\nabla }u{|}^{p-2}\mathrm{\nabla }u\right),1<p<N$ and $\alpha >1/2$ is a parameter. Under suitable conditions on $g(x,u)$, the nonexistence of solutions to Equation (1) is investigated.

中文翻译：

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ℝN 中拟线性薛定谔方程的解不存在

摘要

在本文中，我们研究了拟线性薛定谔方程解的不存在性：(1)$\begin{array}{r}-{\mathrm{\Delta }}_p你+五\left(X\right)|你{|}^{p-2}你-{\mathrm{\Delta }}_p\left(|你{|}^{2\alpha }\right)|你{|}^{2\alpha -2}你=G(X,你),X\in {\mathbb{R}}^{ñ},\end{array}$(1)其中p拉普拉斯算子${\mathrm{\Delta }}_p你=\mathrm{d}\mathrm{一世}\mathrm{v}\left(|\mathrm{\nabla }你{|}^{p-2}\mathrm{\nabla }你\right),1<p<ñ$和$\alpha >1/2$是一个参数。在合适的条件下$G(X,你)$，研究了方程（1）的解不存在。