主要从事时滞微分方程理论与应用研究,在国内外学术杂志发表论文一百多篇,被SCI收录70多篇,荣获安徽省科学技术三等奖(2006年1月和2009年2月)二次,海南省学技术一等奖一次(2009年1月),2006年9月---2006年10月,应邀到南开大学陈省身数学所访问,从事泛函微分方程同宿轨问题研究。完成国家自然科学基金1项. 曾受聘担任
1. SCI期刊《Journal of Applied Mathematics》(Hindawi Publishing Corporation) 编委(2012-2017);
2.《南京信息工程大学学报》(自然科学版)编委(2012-2016);
[1] S.P. Lu and L.J. Chen, The problem of existence of periodic solutions for neutral functional differential system with nonlinear difference operator, J. Math. Anal. Appl.387 (2012) 1127–1136.
[2] Xiang Lv, Shiping Lu, Homoclinic solutions for ordinary p-Laplacian systems,Applied Mathematics and Computation 218 (2012) 5682–5692
[3] S.P. Lu et al, New properties of D-operator and its applications on the problem of periodic solutions to neutral functional differential system, Nonlinear Anal., 74(2011)3011–3021.
[4] 王雯,鲁世平,厄尔尼诺-南方涛动时滞海气振子耦合模型,物理学报,60(2011)030205-1—030205-4.
[5] S.P. Lu, Homoclinic solutions for a nonlinear second order differential system with p-Laplacian operator, Nonlinear Analysis: Real World Appl. 12(2011)525–534.
[6] S.P. Lu, Homoclinic solutions for a class of second-order p-Laplacian differential systems with delay, Nonlinear Anal.: Real World Appl. 12(2011)780–788.
[7] S.P. Lu,The problem of existence of homoclinic solutions to a Rayleigh equation with delay, Proceedings of the 5th Interna ional Congress on Mathematical Biology, Nanjing, P. R. China, June 3-5, 2011.
[8] S.P. Lu Existence of homoclinic solutions to a functional differential equation, 2010 International Conference on Applied Math. and Physics, Nanjing, P. R. China, May 7-9, 2010
[9] Zhengxin Wang, S.P. Lu and Jinde Cao, Existence of periodic solutions for a p-Laplacian neutral functional differential equation with multiple variable parameters, Nonlinear Anal, 72(2010)734-747.
[10] X. Lv, S.P. Lu, P. Yan, Existence of homoclinic solutions for a class of second order Hamiltonian systems, Nonlinear Anal., 72( 2010)390-398.
[11] X. Lv, S. P. Lu, P. Yan, Homoclinic solutions for nonautonomous second-order Hamiltonian s systems with a coercive potential, Nonlinear Anal., 72(2010) 3484-3490.
[12] X. Lv, S.P. Lu, P. Yan, Existence and global attractivity of positive periodic solutions of Lotka-Volterra predator-prey systems with deviating arguments, Nonlinear Anal., Real World Appl., 11(2010)574-583.
[13] X. Lv, P. Yan, S.P. Lu, Existence and global attractivity of positive periodic solutions of competitor-competitor-mutualist Lotka-Volterra systems with deviating arguments, Mathematical and Computer Modelling, 51(2010) 823-832.
[14] 陈丽娟, 鲁世平,零维气候系统非线性模式的周期解问题,物理学报,20(2013)200201-03。
[15] 陈丽娟, 鲁世平,莫嘉琪,磁层-电离层耦合过程中等离子体粒子运动的周期轨,物理学报,9(2013)090201-04。
[16]Lu, Shiping, Existence of periodic solutions for neutral functional differential equations with nonlinear difference operator, Acta Mathematica Sinica-English Series, 32(2016) 1541-1556
[17] Lu, Shiping, Zhong, Tao, Two homoclinic solutions for a nonperiodic fourth-order differential equation without coercive condition, Mathematical Methods in the Applied Sciences, 40(2017) 3163-3172
[18]Fanchao Kong, Shiping Lu, and Zhiguo Luo , Positive periodic solutions for singular higher order delay differential equations, Results in Mathematics, 72 (2017) 71–86
[19]Shiping Lu and Xuewen Jia, Homoclinic solutions for a second-order singular differential equation, Journal of Fixed Point Theory and Applications. (2018) 20:101
[20] Fanchao Kong, Shiping Lu, Zhiguo Luo, Solitary wave and periodic wave solutions of generalized neutral-type neural networks with delays, Neural Process Letters, 48( 2018) 441–458
[21] Lu Shiping;Guo Yuanzhi ; Chen Lijuan, Periodic solutions for Lienard equation with an indefinite singularity, Nonlinear Analysis, Real World Applications, 45(2019) 542-556.
[22] Yu, Xingchen , Shiping, A multiplicity result for periodic solutions of Lienard equations with an attractive singularity, Applied Mathematics and Computation,
346( 2019) 183-192.
1.项目--泛函微分方程周期解与偏差量之间关系研究,荣获2009年安徽省科学技术三等奖,排名第一;
2.项目--微分方程的相关算子理论及其应用研究,荣获2009年海南省科学技术一等奖,排名第三;
3.项目--泛函微分方程周期解问题研究,荣获2006年安徽省科学技术三等奖,排名第一。