论文标题
共振时微分方程系统的无限解决方案
Unbounded solutions to systems of differential equations at resonance
论文作者
论文摘要
我们处理$ x_j'' + n_j^2 \，x_j + h_j（x_1，x_1，\ ldots，x_d）= p_j（t），\ qquad j = 1，\ qquad j = 1，\ ldots，ddots，dd，ddots，ddots，d y_jj $ h_j $ lipschit和can $ conter， $ n_j \ in \ mathbb {n} $（使系统处于共鸣）。通过用于离散动态系统的Lyapunov函数方法，我们证明了无限解决方案的存在，当假定耦合术语上的全局或渐近条件$ H_1，\ ldots，H_D $时。
We deal with a weakly coupled system of ODEs of the type $$ x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots,x_d) = p_j(t), \qquad j=1,\ldots,d, $$ with $h_j$ locally Lipschitz continuous and bounded, $p_j$ continuous and $2π$-periodic, $n_j \in \mathbb{N}$ (so that the system is at resonance). By means of a Lyapunov function approach for discrete dynamical systems, we prove the existence of unbounded solutions, when either global or asymptotic conditions on the coupling terms $h_1,\ldots,h_d$ are assumed.
