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