Abstract In this article, we are concerned with the existence of nontrivial solutions to the Choquard equation <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mo>−</m:mo> <m:mi mathvariant="normal">Δ</m:mi> <m:mi>u</m:mi> <m:mo>+</m:mo> <m:mi>α</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>x</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mi>u</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>x</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> </m:msup> <m:mo>∗</m:mo> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> </m:mrow> </m:msup> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:msup> <m:mrow> <m:mo>∣</m:mo> <m:mi>u</m:mi> <m:mo>∣</m:mo> </m:mrow> <m:mrow> <m:mi>q</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:msup> <m:mi>u</m:mi> <m:mspace width="1.0em"/> <m:mstyle> <m:mspace width="0.1em"/> <m:mtext>in</m:mtext> <m:mspace width="0.1em"/> </m:mstyle> <m:mspace width="0.33em"/> <m:msup> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:msup> <m:mspace width="1em"/> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>N</m:mi> <m:mo>≥</m:mo> <m:mn>2</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>,</m:mo> </m:math> -\Delta u+\alpha \left(x)u=\left({| x| }^{-\mu }\ast {| u| }^{q}){| u| }^{q-2}u\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}\hspace{1em}\left(N\ge 2), with recurrent potential <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha , where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mn>0</m:mn> <m:mo>&lt;</m:mo> <m:mi>μ</m:mi> <m:mo>&lt;</m:mo> <m:mi>N</m:mi> </m:math> 0\lt \mu \lt N and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mfrac> <m:mrow> <m:mn>2</m:mn> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> </m:mrow> </m:mfrac> <m:mo>&lt;</m:mo> <m:mi>q</m:mi> <m:mo>&lt;</m:mo> <m:mfrac> <m:mrow> <m:mn>2</m:mn> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mi>μ</m:mi> </m:mrow> <m:mrow> <m:mi>N</m:mi> <m:mo>−</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mfrac> </m:math> \frac{2N-\mu }{N}\lt q\lt \frac{2N-\mu }{N-2} . Our results include some classical cases where <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha is constant and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha is periodic, as well as some new cases, such as <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha being almost periodic and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>α</m:mi> </m:math> \alpha being only bounded and uniformly continuous.

Hui-Sheng Ding

Quan Liu

Wei Long

Lan Zhong

Advances in Nonlinear Analysis

非线性分析进展 (ANONA) 旨在发表针对来自不同领域的非线性问题的选定研究贡献，特别是那些引入能够解决广泛问题的新技术的研究贡献。该杂志专注于解决纯非线性分析和应用非线性分析中的重大问题的论文。 ANONA 力求向广大读者展示该领域最重要的进展，包括数学、物理和工程领域的研究人员和研究生。

Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions addressing nonlinear problems from various fields, particularly those that introduce new techniques to solve a wide range of issues. The journal focuses on significant papers that tackle major problems in both pure and applied nonlinear analysis. ANONA strives to showcase the most important advancements in the field to a broad audience, including researchers and graduate students in mathematics, physics, and engineering.

《Advances in Nonlinear Analysis》（非线性分析进展）旨在发表来自不同领域的非线性问题的精选研究成果，特别是那些引入新技术以解决广泛问题的研究。该杂志专注于解决纯非线性分析和应用非线性分析中的重大问题，力求向广大读者展示该领域的重要进展，涵盖数学、物理和工程等领域的研究人员和研究生。

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数学	1
数学, 数学	1
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Choquard equations with recurrent potentials

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Category	Quartile
MATHEMATICS, APPLIED	1