主要研究领域是与几何曲率相关的椭圆与抛物型偏微分方程，聚焦于解在无穷远处或孤立奇点附近的定性分析理论。2021年以来，在《Calc. Var. Partial Differential Equations》，《J. Differential Equations》，《Israel J. Math.》，《Adv. Nonlinear Stud.》，《J. Geom. Anal.》，《Nonlinear Anal.》，《Commun. Contemp. Math.》，以及《Commun. Pure Appl. Anal.》等SCI期刊发表10篇学术论文。代表作如下（署名按姓氏排序）：
[1] Jiguang Bao, Yimei Li,Zixiao Liu. Isolated boundary singularities for the fourth ordersubcritical Lane–Emden equations. Calc. Var. Partial Differential Equations, 2025.
[2] Shan Chen,Zixiao Liu. Asymptotic behavior of positive solutions of somenonlinear elliptic equations on cylinders, J. Differential Equations, 2024.
[3] Jiguang Bao,Zixiao Liu, Cong Wang. Existence of Entire Solutions to the Lagrangian MeanCurvature Equations in Supercritical Phase, J. Geom. Anal., 2024.
[4] Ning An, Jiguang Bao,Zixiao Liu. Entire solutions to the parabolic Monge–Ampère equation withunbounded nonlinear growth in time. Nonlinear Anal., 2024.
[5]Zixiao Liu, Jiguang Bao. Symmetry of solutions of minimal gradient graph equations on punctured space. Israel J. Math., 2023.
