Center Manifolds for Non-instantaneous Impulsive Equations Under Nonuniform Hyperbolicity

Li, Mengmeng; Wang, JinRong; O’Regan, Donal; Fečkan, Michal

doi:10.5802/crmath.47

Équations différentielles

Center Manifolds for Non-instantaneous Impulsive Equations Under Nonuniform Hyperbolicity

Li, Mengmeng ¹ ; Wang, JinRong ^1,² ; O’Regan, Donal ³ ; Fečkan, Michal ^4,⁵

¹ Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China
² School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
³ School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
⁴ Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
⁵ Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 341-364.

Résumé

In this paper, we establish the existence of smooth center manifolds for a class of nonautonomous differential equations with non-instantaneous impulses under sufficiently small perturbations of the linear homogeneous part which has a nonuniform exponential trichotomy. In addition, we show the $C^{1}$ smoothness of center manifolds outside the jumping times.

Reçu le : 2019-09-28
Révisé le : 2020-03-24
Accepté le : 2020-03-30
Publié le : 2020-07-10

DOI : 10.5802/crmath.47

Affiliations des auteurs :

Li, Mengmeng ¹ ; Wang, JinRong ^{1, 2} ; O’Regan, Donal ³ ; Fečkan, Michal ^{4, 5}

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     author = {Li, Mengmeng and Wang, JinRong and O{\textquoteright}Regan, Donal and Fe\v{c}kan, Michal},
     title = {Center {Manifolds} for {Non-instantaneous} {Impulsive} {Equations} {Under} {Nonuniform} {Hyperbolicity}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {341--364},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.47},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/crmath.47/}
}

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Li, Mengmeng; Wang, JinRong; O’Regan, Donal; Fečkan, Michal. Center Manifolds for Non-instantaneous Impulsive Equations Under Nonuniform Hyperbolicity. Comptes Rendus. Mathématique, Tome 358 (2020) no. 3, pp. 341-364. doi : 10.5802/crmath.47. http://www.numdam.org/articles/10.5802/crmath.47/

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