郭辉(博士)

2019年11月16日 20:00  点击:[]

郭辉,男,湖南益阳人,博士,副教授,硕士研究生导师,湖南省省青年骨干教师,主要从事微分方程与动力系统方向的研究。主持完成湖南省青年项目1项,主持在研湖南省面上项目和教育厅优青项目各1项,以第一作者和通讯作者身份在《Journal of Differential Equations》、《Nonlinear Analysis》、《Communications in Contemporary Mathematics》、《Journal of Mathematical Analysis and Applications》、《Advanced Nonlinear Studies》、《Advances in Nonlinear Analysis》等国际学术期刊上发表论文20余篇。

一、近年来发表的主要论文

[1]Hui Guo, Tao Wang, Taishan Yi. Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball. J. Differential Equations. 2023,368: 229-246.

[2]Hui Guo, Dan Wu. Nodal solutions for the Schr?dinger-Poisson equations with convolution terms. Nonlinear Anal., 2020, 196: 111781.

[3]Hui Guo, Boling Tang, Tao Wang. Infinitely Many Positive Nonradial Solutions for the Kirchhoff Equation[J]. Mathematical Methods in the Applied Sciences, 2025.DOI:10.1002/mma.10718

[4]Hui Guo, Ronghua Tang, Tao Wang. Infinitely many nodal solutions with a prescribed number of nodes for the Kirchhoff type equations. J. Math. Anal. Appl., 2022,505:125519.

[5]Hui Guo, Ronghua Tang, Tao Wang. Nodal solutions for the Schr¨odinger-Poisson system with an asymptotically cubic term. Math. Methods Appl. Sci. 2022, 45(16):9696-9718.

[6]Hui Guo, Tao Wang. A multiplicity result for a Non-local critical problem. Taiwanese J. Math., 2019, 23(6):1389-1421. 

[7]Hui Guo, Tao Wang. Infinitely Many Solutions for the Nonlinear Schrodinger-Poisson System with Broken Symmetry. Adv. Nonlinear Stud., 2021, 21(3):579-592.

[8]Hui Guo. Nonexistence of least energy nodal solutions for Schr?dinger-Poisson equation. Appl. Math. Lett.,2017, 68: 135-142.

[9]Changfeng Gui, Hui Guo. Nodal solutions of a nonlocal Choquard equation in a bounded domain. Commun. Contemp. Math., 2019, 1950067:1-33.

[10]Changfeng Gui, Hui Guo. On Nodal Solutions of the Nonlinear Choquard Equation. Adv. Nonlinear Stud.,2019, 19(4): 677-691.

[11]Boling Tang, Hui Guo, Tao Wang. Positive multi-bump solutions for the Schr?dinger equation with slow decaying competing potentials[J]. J. Math. Anal. Appl., 2025, 543, 128904.

[12]Meiqi Bao, Hui Guo, Tao Wang. Multi-bumps solutions for the nonlinear Schr?dinger equation under a slowing decaying potential[J]. Mathematical Methods in the Applied Sciences. 2024,47:4430–4448.

[13]Tao Wang, Hui Guo. Existence and nonexistence of nodal solutions for Choquard type equations with perturbation. J. Math. Anal. Appl., 2019, 480(2), 123438.

[14]Tao Wang, Yanling Yang and Hui Guo. Multiple nodal solutions of the Kirchhoff-type problem with a cubic term. Advances in Nonlinear Analysis, 2022, 11: 1030-1047.

[15]Yanling Yang, Tao Wang and Hui Guo. Existence of sign-changing solutions for a gauged nonlinear Schr\"odinger equation with a quintic term. J. Math. Anal. Appl., 2023, 520(1): 126877.

[16]Yonghui Tong, Hui Guo, Giovany M. Figueiredo. Ground state sign-changing solutions and infinitely many solutions for fractional logarithmic Schr?dinger equations in bounded domains. Electron. J. Qual. Theory Differ. Equ., 2021, 70:1-14.

二、近年来主持的课题 

1.主持湖南省自然科学面上基金“非局部Choquard方程多峰解的存在性问题研究”。2024.1-2026.12.

2.主持湖南省青年基金:“薛定谔-泊松方程变号解和非径向解的存在性研究”,2020.1-2022.12

3.主持湖南省教育厅优秀青年项目“薛定谔-泊松方程无穷多解的存在性及其性态研究”。2022.10-2025.9.

三、近年来指导学生获奖情况

1.2022年, 指导全国“田家炳杯”全日制教育硕士专业学位研究生学科教学(数学)专业教学技能大赛获三等奖1项。

2.2023年指导本科生参加全国大学生数学竞赛国家三等奖,省三等奖各一项

3.2023年指导本科生参加全国大学生数学建模省二等奖一项


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