论文标题
通过BOREL可总结功能和Painlevé方程的应用，构建非线性不规则奇异微分方程的解决方案
Construction of solutions of nonlinear irregular singular differential equations by Borel summable functions and an application to Painlevé equations
论文作者
论文摘要
非线性微分方程的系统$ x^{1+γ} \ frac {dy} {dx} = f_0（x）+a（x）y（x）y+f（x，y）$。我们通过在渐近分析中使用Borel可总结函数的理论来更精确地研究转化和解决方案的渐近扩展的含义，并将结果应用于Painlevé方程。
A system of nonlinear differential equations $x^{1+γ}\frac{dY}{dx}= F_0(x)+A(x)Y+F(x,Y)$ is considered. We study more precisely the meaning of asymptotic expansion of transformations and solutions than preceding pioneering works, by using the theory of Borel summable functions in asymptotic analysis, and apply results to Painlevé equations.
