JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 92-96.doi: 10.6040/j.issn.1671-9352.0.2020.084
MA Wei-feng, CHEN Peng-yu*
CLC Number:
| [1] BELLMAN R, COOKE K L. Differential difference equations[M]. New York: Academic Press, 1963. [2] DIEKMANN O. Delay equations: functional, complex and nonlinear analysis[M]. New York: Springer-Verlag, 1995. [3] HALE J K. Theory of functional differential equations[M]. New York: Springer-Link, 1977. [4] BARTHA M. On stability properties for neutral differential equations with state-dependent delay[J]. Journal and Dynamics Differential Equations, 1999, 7(2):197-220. [5] DRIVER R D. A two-body problem of classical electrodynamics: the one-dimensional case[J]. Annals of Physics, 1963, 21(1):122-142. [6] KRISHNAN H P. Existence of unstable manifolds for a certain class of delay differential equations[J]. Electronic Journal of Differential Equations, 2001, 21(1):1-13. [7] KRISZTIN T. A local unstable manifold for differential equations with state-dependent delay[J]. Discrete and Continuous Dynamical Systems, 2003, 9(4):993-1028. [8] KRISZTIN T. C1-smoothness of center manifolds for delay differential equations with state-dependent delay[J]. Proc Amer Math Soc, 2006, 48:213-226. [9] KRISZTIN T, ARINO O. The two-dimensional attractor of a differential equations with state-dependent delay[J]. Journal and Dynamics Differential Equations, 2001, 13(3):453-522. [10] LOUIHI M, HBID M L, ARINO O. Semigroup properties and the Crandall Liggett approximation for a class of differential equations with state-dependent delays[J]. J Differential Equations, 2002, 181(1):1-30. [11] JOHN M P, NUSSBAUM R D, PARASKEVOPOULOS P. Periodic solutions for functional differential equations with multiple state-dependent time lags[J]. Topological Methods in Nonlinear Analysis, 1994, 3(1):101-162. [12] REZOUNENKO A V. Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions[J]. Nonlinear Anal, 2009, 70(11):3978-3986. [13] REZOUNENKO A V. A condition on delay for differential equations with discrete state-dependent delay[J]. J Math Anal Appl, 2012, 385(1):506-516. [14] WALTHER H O. The solution manifold and C1-smoothness for differential equations with state-dependent delay[J]. J Differential Equations, 2003, 195(1):46-65. [15] WALTHER H O. Differentiable semiflows for differential equations with state-dependent delays[J]. Univ Iagel Acta Math, 2003, 1269(41):57-66. [16] WALTHER H O. Smoothness properties of semiflow for differential equations with state-dependent delays[J]. Journal of Mathematical Sciences, 2004, 124(4):5193-5207. [17] HARTUNG F, KRISZTIN T, WALTHER H O, et al. Functional differential equations with state-dependent delay: theory and application[J]. International Journal of Tourism Research, 2006, 13(2):141-163. [18] KRISZTIN T, REAOUNENKO A. Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold[J]. J Differential Equations, 2016, 260(5):4454-4472. [19] LV Yunfei, YUAN Rong, PEI Yongzhen. Smoothness of semiflows for parabolic partial differential equations with state-dependent delay[J]. J Differential Equations, 2016, 260(7):6201-6231. [20] LV Yunfei, PEI Yongzhen, YUAN Rong. Principle of linearized stability and instability for parabolic differential equations with state-dependent delay[J]. J Differential Equations, 2019, 267(3):1671-1704. [21] PAZY A. Semigroups of linear operators and applications to partial differential equations[M]. New York: Springer-Verlag, 1983. |
| [1] | GUO Fei-wang, ZHANG Xi-yong, HAN Wen-bao. A construction of perfect nonlinear functions [J]. J4, 2011, 46(3): 26-30. |
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