论文标题
微分方程超线性系统解决方案的长期行为
Long-time behavior of solutions of superlinear systems of differential equations
论文作者
论文摘要
本文确立了精确的渐近行为，因为时间$ t倾向于无穷大，对于普通微分方程的真正非线性系统的非平凡，衰减的解决方案。当空间变量很小时，这些系统中的最低阶项不是线性的，而是均质的，大于一个的程度。我们证明，对于非零矢量$ξ$和明确的数字$ p> 0 $，我们证明该解决方案的行为例如$ξt^{ - p} $，为$ t \ to \ infty $。
This paper establishes the precise asymptotic behavior, as time $t$ tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the spatial variables are small, is not linear, but rather positively homogeneous of a degree greater than one. We prove that the solution behaves like $ξt^{-p}$, as $t\to\infty$, for a nonzero vector $ξ$ and an explicit number $p>0$.
