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	Boundedness of solutions of nonlinear differential equations
	Liu, B ; Zanolin, F
	1998
关键词	boundedness of solutions quasiperiodic solutions KAM theory reversible systems PERIODIC POTENTIALS REVERSIBLE-SYSTEMS THEOREM
英文摘要	In this paper we are concerned with the boundedness of solutions of some nonlinear differential equations, which are neither dissipative nor conservative, having the form x" + f(x,t)x' + g(x,t) = 0, where f and g are odd polynomials in x with coefficients which are even and periodic in t. Using the KAM theory for reversible systems, we prove that all the solutions are bounded whenever a sharp condition on the degrees of f and g is satisfied. We also obtain a boundedness result when f(x,t) = 0 (i.e., the equation is conservative), under some smoothness assumptions on g which improve the previously known ones. In this case, no symmetry conditions on g are needed. (C) 1998 Academic Press.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000072888500003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics; SCI(E); 13; ARTICLE; 1; 66-98; 144
语种	英语
出处	SCI
出版者	微分方程杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157420]
专题	数学科学学院
推荐引用方式 GB/T 7714	Liu, B,Zanolin, F. Boundedness of solutions of nonlinear differential equations. 1998-01-01.

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