具鞍状势的对数薛定谔方程正解的存在性
偏微分方程分析
2019-04-23 v1
摘要
本文利用 Szulkin \cite{szulkin} 发展的变分方法，证明如下对数薛定谔方程正解的存在性： \left\{ \begin{array}{lc} -{\epsilon}^2\Delta u+ V(x)u=u \log u^2, & \mbox{in} \quad \mathbb{R}^{N}, \\ %u(x)>0, & \mbox{in} \quad \mathbb{R}^{N} \\ u \in H^1(\mathbb{R}^{N}), & \; \\ \end{array} \right. 其中 ，且 为鞍状势。
引用
@article{arxiv.1904.09772,
title = {Existence of a positive solution for a logarithmic Schr\"{o}dinger equation with saddle-like potential},
author = {Claudianor O. Alves and Chao Ji},
journal= {arXiv preprint arXiv:1904.09772},
year = {2019}
}