Về bậc $$[p,q]_{,\varphi }$$ và phương trình vi phân phức

Jianren Long1, Hong‐Yan Qin1, Tao Lei1
1School of Mathematical Science, Guizhou Normal University, Guiyang, 550025, People's Republic of China

Tóm tắt

Tóm tắtGiải pháp phát triển nhanh của phương trình vi phân tuyến tính sau đây $$(*)$$ ( ) được nghiên cứu bằng cách sử dụng một thang số tổng quát hơn $${[p,q]_{,\varphi }}$$ [ p , q ] , φ -bậc, $$\begin{aligned} f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdot \cdot \cdot +A_0(z)f=0,\qquad (*) \end{aligned}$$ f ( k ) + A k - 1 ( z ) f ( k - 1 ) + · · · + A 0 ( z ) f = 0 , ( ) Trong đó $$A_i(z)$$ A i ( z ) là các hàm nguyên trong mặt phẳng phức, $$i=0,1,\ldots ,k-1$$ i = 0 , 1 , , k - 1 . Mối quan hệ tăng trưởng giữa các hệ số nguyên và các giải pháp của phương trình $$(*)$$ ( ) được tìm thấy bằng cách sử dụng các khái niệm về $${[p,q]_{,\varphi }}$$ [ p , q ] , φ -bậc và $${[p,q]_{,\varphi }}$$ [ p , q ] , φ -loại, mở rộng và cải thiện một số kết quả trước đó.

Từ khóa


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