论文标题
确切的扰动存在和独特定理
An Exact Perturbative Existence and Uniqueness Theorem
论文作者
论文摘要
我们研究了$ \ hbar \ hbar \ partial_x f = f（x，x，\ hbar，f）$ \ hbar $的单个扰动的非线性复杂差异系统，其中$ \ hbar $是一个小的复杂扰动参数。在$ f $ jacobian矩阵的特征值上的几何假设下，我们证明了精确扰动溶液的存在和唯一定理；即，$ \ hbar $中有处方扰动扩展的全态解决方案。实际上，这些解决方案是对正式扰动解决方案的鲍尔重新调整。
We investigate singularly perturbed nonlinear complex differential systems of the form $\hbar \partial_x f = F (x, \hbar, f)$ where $\hbar$ is a small complex perturbation parameter. Under a geometric assumption on the eigenvalues of the Jacobian matrix of $F$, we prove an Existence and Uniqueness Theorem for exact perturbative solutions; i.e., holomorphic solutions with prescribed perturbative expansions in $\hbar$. In fact, these solutions are the Borel resummation of the formal perturbative solutions.
