Saved in:
Bibliographic Details
Main Authors: Huang, Chen, Yang, Zhipeng
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.12732
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • In this paper, we consider the following logarithmic Schrödinger equation \[ -Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}. \] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R)\), \(V\) is bounded away from zero, and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative variational approach to overcome the lack of \(C^{1}\)-smoothness of the associated functional and prove the existence and multiplicity of nontrivial weak solutions.