非线性复微分方程的解与H_ω~∞空间

The Solutions of Nonlinear Complex Differential Equations and H_ω~∞ Space

利用直接的积分估计,研究非线性复微分方程(f^(k))^(n_k)+A_(k-1)(z)(f^(k-1))^(n_(k-1))+…+A_1(z)(f′)^(n_1)+A_0(z)f=Ak(z)解的函数空间属性,刻画了方程的解析解,以及它们的导数属于H∞ω空间时系数需要满足的条件.改善及推广了已有的相关结果.

Based on the straightforward integral estimate,the properties of function spaces of solutions of the nonlinear differential equation （f^k）^nk＋Ak-1（z）（f^k-1）^nk-1）＋…＋A1（z）（f＇）^n1＋A0（z）f=Ak（z） are studied.The sufficient conditions of the coefficients for the derivatives and analytic solutions of the above equation to be in Hω^∞ are given in this paper,which improves and extends previous results from Huusko-Korhonen-Reijonen.