Boundedness of semilinear Duffing equations at resonance in a critical situation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Xing, Xiumei¹  Wang, Jun²  Wang, Yiqian³ 

[1] Yili Normal Univ, Sch Math & Stat, Xinjiang 835000, Peoples R China

[2] Hohai Univ, Dept Math & Phys, Changzhou Campus, Changzhou 213000, Peoples R China

[3] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

关键词: Semilinear Duffing equations;    Boundedness;    Canonical transformation;    At resonance;    Critical situation;    Moser's theorem;   

DOI  :  10.1016/j.jde.2018.08.031

来源: Elsevier

【 摘 要 】

In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation (x) over dot + n(2) x g(x) = p(t) with the critical situation that vertical bar integral(2 pi)(0)p(t)e(-int) dt vertical bar = 2 vertical bar g (+infinity) - g (-infinity)vertical bar on g and p, where n is an element of N+, p(t) is periodic and g(x) is bounded. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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