报告题目：Normalized Solutions for Logarithmic Schrödinger Equations on the Lattice Graph

报 告 人：徐雄辉 在读博士研究生（南昌大学）

报告时间：2026年8月4日（星期二）上午9：40-10：00

报告地点：数学科学学院115（大报告厅）  

校内联系人： 朱传喜 教授   联系方式：84708351-8420

报告摘要：This talk concerns the existence, asymptotic behavior, and multiplicity of normalized solutions to a logarithmic Schrödinger equation on the lattice graph $\mathbb{Z}^{N}$, with $\eta>0$, $\mu\geq0$, $p>2$, and prescribed $L^{2}$ mass $a$. Assuming $V(x)\leq V_{\infty}:=\lim_{|x|\to\infty}V(x)\in(-\infty,\infty]$, we prove that there exists a threshold $\bar{a}>0$ such that the constrained ground-state level is attained for every $a>\bar{a}$. We also analyze the limiting behavior of ground states as $\mu\to0$. The variational problem presents two key obstacles: the associated energy functional is not of class $C^{1}$ on $H^{1}(\mathbb{Z}^{N})$, and the lack of scaling invariance on the lattice prevents the use of the classical Poho\v{z}aev identity. To address these issues, we construct a well-behaved auxiliary function for the nonlinear term and introduce a family of approximating problems in a broader functional setting. This approach avoids imposing the additional condition $\int_{\mathbb{Z}^{N}}u^{2}|\log u^{2}|\,d\sigma<\infty$. Finally, when the potential is coercive, we establish the existence of infinitely many normalized solutions.

报告人简介：徐雄辉，南昌大学数学与计算机学院在读博士研究生，主要从事非线性泛函分析与偏微分方程的研究，已在Z. Angew. Math. Phys.，Bull. Malays. Math. Sci. Soc.和Nonlinear Anal.杂志上发表论文3篇