一类ODE的最优一致估计和超越所有阶的严格渐近性
Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ODE's
摘要：
对于一阶微分方程$y'=\sum_{p=0}^P F_p(x)y^p$和二阶齐次线性微分方程$y''+a(x)y'+b(x)y=0$，当$|x|\to\infty$在射线$\arg(x)=$上为常数时，其局部可积系数具有渐近（可能发散）幂级数，在进一步的假设下，证明了在给定射线上，真解与（完全）形式解之间存在一一对应.对应关系是基于渐近不等式，要求是均匀的$x$和最佳的某些权重。
英文摘要：
For first order differential equations of the form $y'=\sum_{p=0}^P F_p(x)y^p$ and second order homogeneous linear differential equations $y''+a(x)y'+b(x)y=0$ with locally integrable coefficients having asymptotic (possibly divergent) power series when $|x|\to\infty$ on a ray $\arg(x)=$const, under some further assumptions, it is shown that, on the given ray, there is a one-to-one correspondence between true solutions and (complete) formal solutions. The correspondence is based on asymptotic inequalities which are required to be uniform in $x$ and optimal with respect to certain weights.
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