一类半线性Duffing方程解的有界性

A Kind of Semilinear Duffing Equations's Solution Boundedness

借助一个非线性变换,在一定的假设下,利用Moser小扭转定理重新证明方程x''+ n2 x+φ(x)=p(t)所有解都是有界的,这一方法可极大地简化文献[1]中定理1的证明.

We use a non-linear sympletic transformation reprove prove the all solutions boundedness for semilinear Duffing equation x^″＋n^2x＋φ（x）=p（t） in this paper, this method greatly symplied the prove of theorem 1 in documents[l]