The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation  

作　　者：Yanmei Sun Xiong Li 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University [2]School of Mathematics and Information Sciences, Weifang University

出　　处：《Science China Mathematics》2018年第9期1589-1602,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.11571041);the Fundamental Research Funds for the Central Universities

摘　　要：In this paper, we construct a continuous positive periodic function p(t) such that the corresponding superlinear Duffing equation x′′+ a(x)^(x2n+1)+p(t)x^(2m+1)= 0, n + 2≤2 m+1<2n+1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a(x) is an arbitrary positive smooth periodic function defined in the whole real axis.In this paper, we construct a continuous positive periodic function p（t） such that the corresponding superlinear Duffing equation x″＋ a（x）x^2n＋1＋p（t）x^2m＋1= 0, n ＋ 2≤2 m＋1〈2n＋1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a（x） is an arbitrary positive smooth periodic function defined in the whole real axis.

关 键 词：superlinear Duffing equations BLOW-UP quasi-periodic solutions 

分 类 号：O175[理学—数学]