Research Areas:The study of dynamic systems and nonlinear analysis focuses more on mathematical
problems with physical background. A series of progress has been made in the index theory of
Hamiltonian systems, N-body problem, stability problem and spectral problem of Hamiltonian differential
operators.
0531-88363959
xjhu@sdu.edu.cn
1999.09-2002.06, PhD in Pure Mathematics, Nankai University
1997.09-1999.06, MSc in Pure Mathematics, Jilin University
1993.09-1997.06, BSc in Mathematics, Jilin University
2002.07-2008.06, School of Mathematics, Chinese Academy of Sciences
2008.06-present, School of Mathematics, Shandong University
2005, Second Prize of the 2004 National Natural Science Award (Fourth completer)
2013, Candidates of “New Century Excellent Talents Support Program” of the Ministry of Education
2014, The National Science Fund for Distinguished Young Scholars
2018, Special government allowances of the State Council
2019, Middle-aged Expert with Outstanding Contribution in Shandong Province
2023, First Prize of the 2022 Outstanding Achievement Award for Scientific Research in Institutions of Higher Learning (Science and Technology) of the Ministry of Education (First Place)
36. Hu, Xijun; Ou, Yuwei; Tang, Xiuting Linear stability of an elliptic relative equilibrium in the spatial n-body problem via index theory. Regul. Chaotic Dyn. 28 (2023), no. 4-5, 731–755.
35. Hu, Xijun; Liu, Lei; Wu, Li; Zhu, Hao; On the jth eigenvalue of Sturm-Liouville problem and the Maslov index. J. Dynam. Differential Equations 34 (2022), no. 3, 1949–1967.
34. Hu, Xi Jun; Wu, Li Mean index for non-periodic orbits in Hamiltonian systems. Acta Math. Sin. (Engl. Ser.) 38 (2022), no. 1, 291–310.
33. Hu, Xijun; Ou, Yuwei; Wang, Penghui; Zhu, Hao; Hill-type formula and Krein-type trace formula for Hamiltonian systems. Anal. Theory Appl. 37 (2021), no. 1, 74–101.
32. Hu, Xijun; Ou, Yuwei; Yu, Guowei; An Index Theory for Collision, Parabolic and Hyperbolic Solutions of the Newtonian n-body Problem. Arch. Ration. Mech. Anal. 240 (2021), no. 1, 565–603.
31. Hu, Xijun; Wu, Li; Decomposition of spectral flow and Bott-type iteration formula. Electron. Res. Arch. 28 (2020), no. 1, 127–148.
30. Hu, Xijun; Portaluri, Alessandro; Xing, Qin; Morse Index and Stability of the Planar N-vortex Problem. Qual. Theory Dyn. Syst. 19 (2020), no. 2, 76.
29. Hu, Xijun; Long, Yiming; Ou, Yuwei; Linear stability of the elliptic relative equilibrium with (1 + n)-gon central configurations in planar n-body problem. Nonlinearity 33 (2020) 1016–1045.
28. Barutello, Vivina L.; Hu, Xijun; Portaluri, Alessandro; Terracini, Susanna; An index theory for asymptotic motions under singular potentials. Adv. Math. 370 (2020), 107230.
27. Hu, Xijun; Portaluri, Alessandro; Yang, Ran; A dihedral Bott-type iteration formula and stability of symmetric periodic orbits. Calc. Var. Partial Differential Equations 59 (2020), no. 2, Paper No. 51.
26. Hu, Xijun; Wu, Li; Yang, Ran; Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit. J. Dynam. Differential Equations 32 (2020), no. 1, 61–84.
25. Hu, Xijun; Portaluri, Alessandro; Yang, Ran; Instability of semi-Riemannian closed geodesics. Nonlinearity 32 (2019), no. 11, 4281–4316.
24. Hu, Xijun; Portaluri, Alessandro; Bifurcation of heteroclinic orbits via an index theory. Math. Z. 292 (2019), no. 1-2, 705–723.
23. Hu, Xijun; Ou, Yuwei; Wang, Penghui; Hill-type formula for Hamiltonian system with Lagrangian boundary conditions. J. Differential Equations 267 (2019), no. 4, 2416–2447.
22. Hu, Xijun; Liu, Lei; Wu, Li; Zhu, Hao; Singularity of the $n$-th eigenvalue of high dimensional Sturm–Liouville problems. J. Differential Equations 266 (2019), no. 7, 4106–4136.
21. Hu, Xijun; Yu, Guowei; An index theory for zero energy solutions of the planar anisotropic Kepler problem. Comm. Math. Phys. 361 (2018), no. 2, 709–736.
20. Hu, Xijun; Portaluri, Alessandro; Index theory for heteroclinic orbits of Hamiltonian systems. Calc. Var. Partial Differential Equations 56 (2017), no. 6, Art. 167, 24 pp.
19. Hu, Xijun; Ou, Yuwei Stability of closed characteristics on compact convex hypersurfaces in $\bold{R}^{2n}$. J. Fixed Point Theory Appl. 19 (2017), no. 1, 585–600.
18. Hu, Xijun; Ou, Yuwei; Collision index and stability of elliptic relative equilibria in planar $n$-body problem. Comm. Math. Phys. 348 (2016), no. 3, 803–845.
17. Hu, Xijun; Wang, Penghui; Eigenvalue problem of Sturm-Liouville systems with separated boundary conditions. Math. Z. 283 (2016), no. 1-2, 339–348.
16. Hu, Xijun; Wang, Penghui; Hill-type formula and Krein-type trace formula for $S$-periodic solutions in ODEs. Discrete Contin. Dyn. Syst. 36 (2016), no. 2, 763–784.
15.Hu, Xijun; Ou, Yuwei; Wang, Penghui; Trace formula for linear Hamiltonian systems with its applications to elliptic Lagrangian solutions. Arch. Ration. Mech. Anal.216 (2015), no. 1, 313–357.
14. Hu, Xijun; Long, Yiming; Sun, Shanzhong; Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory. Arch. Ration. Mech. Anal. 213 (2014), no. 3, 993–1045.
13. Chen, Chao-Nien; Hu, Xijun; Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations. Calc. Var. Partial Differential Equations 49 (2014), no. 1-2, 827–845.
12. Hu, Xijun; Wang, Penghui; Conditional Fredholm determinant and trace formula for Hamiltonian systems: a survey. Emerging topics on differential equations and their applications, 12–23, Nankai Ser. Pure Appl. Math. Theoret. Phys., 10, World Sci. Publ., Hackensack, NJ, 2013.
11. Hu, Xijun; Ou, Yuwei; An estimation for the hyperbolic region of elliptic Lagrangian solutions in the planar three-body problem. Regul. Chaotic Dyn. 18 (2013), no. 6,732–741.
10. Hu, Xijun; Wang, Penghui Conditional Fredholm determinant for the $S$-periodic orbits in Hamiltonian systems. J. Funct. Anal. 261 (2011), no. 11, 3247–3278.
9.Hu, Xijun; Sun, Shanzhong Variational principle and linear stability of periodic orbits in celestial mechanics. Progress in variational methods, 40–51, Nankai Ser. Pure Appl. Math. Theoret. Phys., 7, World Sci. Publ., Hackensack, NJ, 2011.
8. Hu, XiJun; Sun, ShanZhong Morse index and the stability of closed geodesics. Sci. China Math. 53 (2010), no. 5, 1207–1212.
7. Hu, Xijun; Sun, Shanzhong Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem. Adv. Math. 223 (2010), no. 1, 98–119.
6. Hu, Xijun; Sun, Shanzhong Stability of relative equilibria and Morse index of central configurations. C. R. Math. Acad. Sci. Paris 347 (2009), no. 21-22, 1309–1312.
5. Hu, Xijun; Sun, Shanzhong Index and stability of symmetric periodic orbits in Hamiltonian systems with application to figure-eight orbit. Comm. Math. Phys. 290(2009), no. 2, 737–777.
4. Chen, Chao-Nien; Hu, Xijun Stability criteria for reaction-diffusion systems with skew-gradient structure. Comm. Partial Differential Equations 33 (2008), no. 1-3,189–208.
3. Wang, Wei; Hu, Xijun; Long, Yiming Resonance identity, stability, and multiplicity of closed characteristics on compact convex hypersurfaces. Duke Math. J. 139(2007), no. 3, 411–462.
2. Chen, Chao-Nien; Hu, Xijun Maslov index for homoclinic orbits of Hamiltonian systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007), no. 4, 589–603.
1. Hu, Xijun; Long, Yiming Closed characteristics on non-degenerate star-shaped hypersurfaces in $\Bbb R^{2n}$. Sci. China Ser. A 45 (2002), no. 8, 1038–1052.
1. Celestial mechanics-N-body problem, National Key Research and Development Program of the Ministry of Science and Technology, 2020.11.30-2025.11.30.
2. The study of singular orbits in Hamiltonian systems, National Natural Science Foundation of China (General Program),2020.09.18-2024.12.31
