摘要
结合解析函数空间理论及复微分方程理论,讨论非齐次线性复微分方程f^((k))+Bk-1(z)f^((k-1))+…+B1(z)f'+B_(0)(z)f=B_(k)(z)解析解的性质.首先,得到了方程解析解属于加权Bergman空间(A_(ω)^(p))的系数条件;其次讨论了其逆问题,即当方程所有解属于加权Bergman空间(A_(ω)^(p))时系数属于加权Bergman空间A_(ω_([kp]))^(p);最后讨论了二阶齐次微分方程解的加权Bergman空间(A_(2(ρ+2))^(p))性质.
In this paper,the properties of the analytic solution of the nonhomogeneous linear complex differential equation f^((k))+Bk-1(z)f^((k-1))+…+B1(z)f'+B_(0)(z)f=B_(k)(z)is discussed by combining the theory of analytic function space and complex differential equation.Firstly,the condition of coefficients belonging to the weighted Bergman space(A_(ω)^(p))is obtained.Secondly,the inverse problem is discussed,that is,the coefficients belong to the weighted Bergman space A_(ω_([kp]))^(p) when all the solutions belong to the weighted Bergman space.(A_(ω)^(p)Finally,the properties of weighted Bergman space(A_(2(ρ+2))^(p))for solutions of second-order homogeneous differential equations are discussed.
作者
张鹏
李明金
邰祝英
ZHANG PENG;LI MINGJIN;TAI ZHUYING(School of Mathematical Sciences,Guizhou Normal University,Guiyang 550025,China)
出处
《应用数学学报》
北大核心
2025年第6期899-909,共11页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金项目(编号:12261023,11861023)
贵州师范大学学术新苗培养及创新探索专项项目(编号:黔科合平台人才[2018]5769-05号)资助。
