主持科研项目
9.2020-2023,奇异Hamilton系统谱及其相关研究，国家自然科学基金面上项目 8.2015-2018,奇异J-对称哈密顿系统谱问题研究,国家自然科学基金面上项目 7.2012-2014,非对称线性差分系统谱理论研究,国家自然科学基金青年项目 6.2019-2022,奇异线性Hamilton系统谱的研究及其应用,山东省自然科学基金面上项目 5.2011-2013,非自伴线性哈密顿系统谱性质的研究,山东省自然科学基金青年项目 4.2014-2016,奇异J-对称微分算子的谱问题,中国博士后基金面上项目 3.2013-2015,奇异哈密顿算子谱分布研究,山东省博士后创新基金 2.2015-2019,低松弛预应力钢绞线松弛试验数据线性回归模型，威海市科技局 1.2011-2013,奇异微分算子谱定性分析的相关研究,山东大学自主创新项目 六、参与科研项目 6.2018-2021,非局部Sturm-Liouville 谱问题及相应极值问题的研究，国家自然科学基金面上项目（第二位） 5.2017-2019,关于分数阶微分方程谱问题的研究，国家自然科学基金青年项目（第二位） 4.2021-2022,二阶微分算子在有限谱信息下最优恢复问题的研究，山东省自然科学基金面上项目（第三位） 3.2016-2019,Strum-Liouville谱理论中势函数与权函数极值问题的研究，山东省自然科学基金面上项目（第三位） 2.2015-2017,可压流体力学方程组弱(强)解的适定性及其大时间行为,山东省自然科学基金面上项目（第二位） 1.2009-2011,哈密顿微分算子的非相对紧扰动及其应用，山东省自然科学基金面上项目（第三位） |
八、发表论文及著作 [31] Zhu Li, Sun Huaqing, Essential numerical ranges of linear relations and singular discrete linear Hamiltonian systems, Chin. Ann. Math. Ser. B. Accepted. [30] Zhu Li, Sun Huaqing, Xie Bing, On classification of singular matrix difference equations of mixed order, Proc. Roy. Soc. Edinburgh A. 2023, DOI: 10.1017/ prm. 2023.56. [29] Zhang Shuo, Sun Huaqing, Yang Chen, Friedrichs extensions of a class of disc- rete Hamiltonian systems with one singular endpoint, Math. Nachr. 296 (2023), 4169-4191. [28] Zhu Li, Sun Huaqing, On essential numerical ranges and essential spectra of Hamiltonian systems with one singular endpoint, Linear Algebra Appl. 645 (2022), 9-29. [27] Yang Chen, Sun Huaqing, Essential spectra of singular Hamiltonian differential operators of arbitrary order under a class of perturbations, Stud. Appl. Math. 147 (2021), 209-229. [26] Yang Chen, Sun Huaqing, Friedrichs extensions of a class of singular Hamiltonian systems, J. Differential Equations. 293 (2021), 359-391. [25] Sun Huaqing, Xie Bing, Spectra of a class of non-symmetric operators in Hilbert spaces with applications to singular differential operators, Proc. Roy. Soc. Edinburgh A.150 (2020), 1769-1790. [24] Sun Huaqing, Qi Jiangang, Stability of essential spectra of singular Sturm-Liouville differential operators under perturbations small at infinity, Math. Methods Appl. Sci. 41 (2018) 2031-2038. [23] Xie Bing, Sun Huaqing, Guo Xinwei, Non-real eigenvalues of symmetric Sturm-Liouville problems with indefinite weight functions, Electron J Qual Theo. 2 (2017) 1-14. [22] Qi Jiang, Sun Huaqing, Relatively bounded and relatively compact perturbations for limit circle Hamiltonian systems, Integr. Equ. Oper. Theory 86 (2016), 359–375. [21] Sun Huaqing, Kong Qingkai, Shi Yuming, Essential spectrum of singular disc- rete linear Hamiltonian systems, Math. Nachr. 289, (2016), No. 2–3, 343–359. [20] Sun Huaqing, Shi Yuming, On essential spectra of singular linear Hamiltonian systems, Linear Algebra Appl. 469 (2015), 204-229. [19] Sun Huaqing, Shi Yuming, Jian Wenwen, J-self-adjoint extensions of a class of Hamiltonian differential systems, Linear Algebra Appl. 462, (2014), 204-232. [18] Jian Wenwen, Sun Huaqing, On bounds of eigenvalues of complex Sturm-Liouville boundary value problems, Abstr. Appl. Anal. 2014, Art. ID 362340, 4 pp. [17] Sun Huaqing, Shi Yuming, Spectral properties of singular discrete linear Hamiltonian systems, J. Difference Equ. Appl. 20 (2014), no. 3, 379–405. [16] Sun Huaqing, Simplicity and spectrum of singular Hamiltonian systems of arbitrary order, Abstr. Appl. Anal. 2013, Art. ID 202851, 6 pp. [15] Ren Guojing, Sun Huaqing, J-self-adjoint extensions for a class of discrete linear Hamiltonian systems, Abstr. Appl. Anal. 2013, Art. ID 904976, 19 pp. [14] Sun Huaqing, Ren Guojing, J-self-adjoint extensions for second-order linear difference equations with complex coefficients, Adv. Difference Equ. 2013, 2013:3, 26 pp. [13] Sun Huaqing, Qi Jiangang, Criteria of the three cases for non-self-adjoint singular Sturm-Liouville difference equations, J. Difference Equ. Appl. 18 (2012), no. 12, 2069–2087. [12] Sun Huaqing, Qi Jiangang, The theory for J-Hermitian subspaces in a product space, ISRN Math. Anal. 2012, Art. ID 676835, 16 pp. [11] Qi Jiangang, Zheng Zhaowen, Sun Huaqing, Classification of Sturm-Liouville differential equations with complex coefficients and operator realizations, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467 (2011), no. 2131, 1835–1850. [10] Sun Huaqing, Qi Jiangang, Jing Haibin, Classification of non-self-adjoint singular Sturm-Liouville difference equations, Appl. Math. Comput. 217 (2011), no. 20, 8020–8030. [9] Sun Huaqing, Shi Yuming, Self-adjoint extensions for singular linear Hamiltonian systems, Math. Nachr. 284 (2011), no. 5-6, 797–814. [8] Shi Yuming, Sun Huaqing, Self-adjoint extensions for second-order symmetric linear difference equations, Linear Algebra Appl. 434 (2011), no. 4, 903–930. [7] Sun Huaqing, Qi Jiangang, On classification of second-order differential equations with complex coefficients, J. Math. Anal. Appl. 372 (2010), no. 2, 585–597. [6] Sun Huaqing, Shi Yuming, Self-adjoint extensions for linear Hamiltonian systems with two singular endpoints, J. Funct. Anal. 259 (2010), no. 8, 2003–2027. [5] Sun Huaqing, Limit point criteria for singular linear discrete Hamiltonian systems, (Chinese) J. Shandong Univ. Nat. Sci. 45 (2010), no. 3, 76–79. [4] Sun Huaqing, On the limit-point case of singular linear Hamiltonian systems, Appl. Anal. 89 (2010), no. 5, 663–675. [3] Sun Huaqing, Shi Yuming, Strong limit point criteria for a class of singular discrete linear Hamiltonian systems, J. Math. Anal. Appl. 336 (2007), no. 1, 224–242. [2] Sun Huaqing, Shi Yuming, Limit-point and limit-circle criteria for singular second-order linear difference equations with complex coefficients, Comput. Math. Appl. 52 (2006), no. 3-4, 539–554. [1] Sun Huaqing, Shi Yuming, Eigenvalues of second-order difference equations with coupled boundary conditions, Linear Algebra Appl. 414 (2006), no. 1, 361–372.
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