非线性复微分方程与加权Bergman空间  

The nonlinear differential equation and weighted Bergman space

作　　者：孙雪芳 李明金 徐江 SUN Xue-fang;LI Ming-jin;XU Jiang(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China)

机构地区：[1]贵州师范大学数学科学学院,贵州贵阳550025

出　　处：《东北师大学报（自然科学版）》2024年第3期11-17,共7页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12261023,11861023);贵州师范大学学术新苗培养及创新探索专项项目(黔科合平台人才[2018]5769-05号).

摘　　要：结合解析函数空间理论及复微分方程理论,讨论了非线性非齐次复微分方程(f(k))^(n)_(k)+B_(k-1)(f^((k-1)))^(n)_(k)-1+…+B_(1)(f′)^(n)_(1)+B_(0)f=B_(k)解析解的性质,得到了方程解析解属于加权Bergman空间A pω的系数条件.The properties of analytic solutions of the nonlinear nonhomogeneous complex differential equation(f(k))^(n)_(k)+B_(k-1)(f^((k-1)))^(n)_(k)-1+…+B_(1)(f′)^(n)_(1)+B_(0)f=B_(k) is discussed by combining the theory of analytic function space and theory of complex differential equation,the coefficient condition that the analytical solution belongs to the weighted Bergman space(A pω)is obtained.

关 键 词：非线性复微分方程 单位圆 加权BERGMAN空间 解析函数 

分 类 号：O174.52[理学—数学]