一类二阶时滞微分方程多重周期解Multiple Periodic Solutions to a Class of Second-order Differential Equations with Delays
陈业,鲁世平
摘要(Abstract):
利用变分原理和Z2不变群指标对一类二阶时滞微分方程(a(t)x′(t-τ))′-b(t)x(t-)τ+fλ(t,x(t),x(t-)τ,x(t-2)τ)=0的周期解问题进行研究,得出在一些条件下方程有2n个周期为2π的非平凡周期解。
关键词(KeyWords): 变分原理;Z2不变群指标;临界点
基金项目(Foundation): 教育部科学技术重点项目(207047)资助
作者(Author): 陈业,鲁世平
参考文献(References):
- [1]S.P.Lu.Periodic solutions to a second order-Laplacian neutral functional differential system[J].Nonlinear Anal.2008(69):4 215-4 229.
- [2]X.Li,Z.H.Zhang.Periodic solutions for second-order differential equations with a singular nonlinearity[J].Nonlinear Anal.2008(69):3 866-3 876.
- [3]J.Wu,Z.C.Wang.Two periodic solutions of second-order neutral functional differential equations[J].J.Math.Anal.Appl.2007(329):677-689.
- [4]D.Y.Zheng,Z.H.Wang.Periodic solutions of sublinear differential equations[J].J.Math.Anal.Appl.2007(330):1 478-1487.
- [5]Y.T.Xu,Z.M.Guo.Existence of periodic solutions to second-order Hamiltonian systems with potential indefinite in sign[J].Non-linear Anal.2002(51):1 273-1 283.
- [6]Y.T.Xu,Z.M.Guo.Applications of a index theory to periodic solutions for a class of functional differential equations[J].J.Math.Anal.Appl.2001(257):189-205.
- [7]Y.T.Xu,Z.M.Guo.Applications of a geometrical index theory to functional differential equations(in Chinese)[J].Acta Mathemat-ica Sinica,2001(44):1 027-1 036.
- [8]X.B.Shu,Y.T.Xu.Multiple periodic solutions to a class of second-order functional differential equations of mixed type[J].ActaMathematicae Applicatae Sinica,2006,29(5):821-831.
- [9]C.K.Ching.Critical Point Theory and Its Applications(in Chinese)[M].Shanghai scientific and Technical Publishers,Shanghai,1986.
- [10]X.B.Shu,Y.T.Xu,L.H.Huang.Infinite periodic solutions to a class of second-order Sturm-Liouville neutral differential e-quations[J].Nonlinear Anal.2008(68):905-911.
- [11]J.Mawhin,M.Willem.Critical Point Theory and Hamiltonian Systems[M].Springer-Verlag,New York Inc.,1989.