带 Hartree 型非线性项的对数 Schrödinger 方程解的存在性——献给邓引斌教授 70 寿辰

Abstract

Abstract:

We consider the following logarithmic Schrödinger equation with Hartree-type nonlinearity

$ \left\{\begin{array}{l} -\Delta u+V(x) u-\phi u=u \log u^{2}, x \in \mathbb{R}^{3}, \\ -\Delta \phi=u^{2}, \phi \in D^{1,2}\left(\mathbb{R}^{3}\right), \end{array}\right. $

where $V(x) \in C\left(\mathbb{R}^{3}\right)$ is a nonnegative potential function．By using direction derivative and constrained minimization method, we prove the existence of solutions under different types of potentials.

Key words: logarithmic Schr?dinger equations, Hartree-type nonlinearity, the Nehari method

CLC Number:

O175.25

Keheng Chen, Huirong Pi. The Existence of Solutions for the Logarithmic Schrödinger Equation with Hartree-Type Nonlinearity[J].Acta mathematica scientia,Series A, 2026, 46(4): 1505-1512.

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References 19

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The Existence of Solutions for the Logarithmic Schrödinger Equation with Hartree-Type Nonlinearity

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