-
Previous Article
Turing type instability in a diffusion model with mass transport on the boundary
- DCDS Home
- This Issue
-
Next Article
Perturbative techniques for the construction of spike-layers
Asymptotic homogenization for delay-differential equations and a question of analyticity
1. | Division of Applied Mathematics, Brown University, Providence, RI 02912, USA |
2. | Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA |
$ +\infty $ |
$ t\to\pm\infty $ |
$ x'(t) = \sin (t^q)x(t-1) \qquad\text{and}\qquad x'(t) = e^{it^q}x(t-1), \;\;\;\;\;\;\;\;{(*)} $ |
$ q\ge 2 $ |
$ \lim\limits_{t\to-\infty}x(t) = x_- $ |
$ -\infty $ |
$ \lim\limits_{t\to+\infty}x(t) = x_+ $ |
$ +\infty $ |
$ (-\infty,-T] $ |
$ x: \mathbb{R}\to \mathbb{C} $ |
$ (*) $ |
$ x_\pm $ |
$ \pm\infty $ |
$ C^\infty $ |
$ (*) $ |
$ \{z\in \mathbb{C}\:|\: \mathop{{{\rm{Im}}}} z<0\} $ |
References:
[1] |
N. G. de Bruijn, Asymptotic Methods in Analysis, Dover Publications, Inc., New York, 1981. |
[2] |
J. Dieudonné, Foundations of Modern Analysis, Pure and Applied Mathematics, Vol. 10-I, Academic Press, New York-London, 1969.
![]() |
[3] |
J. Mallet-Paret and R. D. Nussbaum,
Analyticity and nonanalyticity of solutions of delay-differential equations, SIAM J. Math. Anal., 46 (2014), 2468-2500.
doi: 10.1137/13091943X. |
[4] |
J. Mallet-Paret and R. D. Nussbaum,
Intricate structure of the analyticity set for solutions of a class of integral equations, J. Dynam. Differential Equations, 31 (2019), 1045-1077.
doi: 10.1007/s10884-019-09746-1. |
[5] |
J. Mallet-Paret and R. D. Nussbaum, Analytic solutions of delay-differential equations, in preparation. Google Scholar |
[6] |
R. D. Nussbaum,
Periodic solutions of analytic functional differential equations are analytic, Michigan Math. J., 20 (1973), 249-255.
doi: 10.1307/mmj/1029001104. |
[7] |
A. Zygmund, Trigonometric Series, Vols. I, II, 2nd edition, Cambridge Univ. Press, New York, 1959. |
show all references
References:
[1] |
N. G. de Bruijn, Asymptotic Methods in Analysis, Dover Publications, Inc., New York, 1981. |
[2] |
J. Dieudonné, Foundations of Modern Analysis, Pure and Applied Mathematics, Vol. 10-I, Academic Press, New York-London, 1969.
![]() |
[3] |
J. Mallet-Paret and R. D. Nussbaum,
Analyticity and nonanalyticity of solutions of delay-differential equations, SIAM J. Math. Anal., 46 (2014), 2468-2500.
doi: 10.1137/13091943X. |
[4] |
J. Mallet-Paret and R. D. Nussbaum,
Intricate structure of the analyticity set for solutions of a class of integral equations, J. Dynam. Differential Equations, 31 (2019), 1045-1077.
doi: 10.1007/s10884-019-09746-1. |
[5] |
J. Mallet-Paret and R. D. Nussbaum, Analytic solutions of delay-differential equations, in preparation. Google Scholar |
[6] |
R. D. Nussbaum,
Periodic solutions of analytic functional differential equations are analytic, Michigan Math. J., 20 (1973), 249-255.
doi: 10.1307/mmj/1029001104. |
[7] |
A. Zygmund, Trigonometric Series, Vols. I, II, 2nd edition, Cambridge Univ. Press, New York, 1959. |
[1] |
Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1103-1110. doi: 10.3934/dcdss.2020392 |
[2] |
Julian Tugaut. Captivity of the solution to the granular media equation. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021002 |
[3] |
Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159 |
[4] |
Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020440 |
[5] |
Yongxiu Shi, Haitao Wan. Refined asymptotic behavior and uniqueness of large solutions to a quasilinear elliptic equation in a borderline case. Electronic Research Archive, , () : -. doi: 10.3934/era.2020119 |
[6] |
Sihem Guerarra. Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation AXB = C. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 75-86. doi: 10.3934/naco.2020016 |
[7] |
Taige Wang, Bing-Yu Zhang. Forced oscillation of viscous Burgers' equation with a time-periodic force. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1205-1221. doi: 10.3934/dcdsb.2020160 |
[8] |
José Luiz Boldrini, Jonathan Bravo-Olivares, Eduardo Notte-Cuello, Marko A. Rojas-Medar. Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations. Electronic Research Archive, 2021, 29 (1) : 1783-1801. doi: 10.3934/era.2020091 |
[9] |
Shuxing Chen, Jianzhong Min, Yongqian Zhang. Weak shock solution in supersonic flow past a wedge. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 115-132. doi: 10.3934/dcds.2009.23.115 |
[10] |
Oussama Landoulsi. Construction of a solitary wave solution of the nonlinear focusing schrödinger equation outside a strictly convex obstacle in the $ L^2 $-supercritical case. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 701-746. doi: 10.3934/dcds.2020298 |
[11] |
Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020172 |
[12] |
Wei Feng, Michael Freeze, Xin Lu. On competition models under allee effect: Asymptotic behavior and traveling waves. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5609-5626. doi: 10.3934/cpaa.2020256 |
[13] |
Yi An, Bo Li, Lei Wang, Chao Zhang, Xiaoli Zhou. Calibration of a 3D laser rangefinder and a camera based on optimization solution. Journal of Industrial & Management Optimization, 2021, 17 (1) : 427-445. doi: 10.3934/jimo.2019119 |
[14] |
Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Fractional optimal control problems on a star graph: Optimality system and numerical solution. Mathematical Control & Related Fields, 2021, 11 (1) : 189-209. doi: 10.3934/mcrf.2020033 |
[15] |
Kai Zhang, Xiaoqi Yang, Song Wang. Solution method for discrete double obstacle problems based on a power penalty approach. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021018 |
[16] |
Yoichi Enatsu, Emiko Ishiwata, Takeo Ushijima. Traveling wave solution for a diffusive simple epidemic model with a free boundary. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 835-850. doi: 10.3934/dcdss.2020387 |
[17] |
Stefan Ruschel, Serhiy Yanchuk. The spectrum of delay differential equations with multiple hierarchical large delays. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 151-175. doi: 10.3934/dcdss.2020321 |
[18] |
Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020107 |
[19] |
Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3467-3484. doi: 10.3934/dcds.2020042 |
[20] |
Yichen Zhang, Meiqiang Feng. A coupled $ p $-Laplacian elliptic system: Existence, uniqueness and asymptotic behavior. Electronic Research Archive, 2020, 28 (4) : 1419-1438. doi: 10.3934/era.2020075 |
2019 Impact Factor: 1.338
Tools
Metrics
Other articles
by authors
[Back to Top]