On the hyper-order of solutions of a class of higher order linear differential equations

作者：Hamani Karima^*; Belaidi Benharrat

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2013, 20(1): 27-39.

• Linear differential equation
• meromorphic function
• hyper-order

In this paper, we investigate the growth of solutions of the linear differential equation
f((k)) + (A(k-1)(2)e(Pk-1(z)) + Bk-1(z)) f((k-1)) + ... +
(A(1)(z)e(P1(z)) + B-1(z)) f' + (A(0)(z)e(P0(z)) + B-0(z)) f = 0,
where k >= 2 is an integer, P-j(z) (j = 0,1, ... ,k - 1) are nonconstant polynomials and A(j)(z) (not equivalent to 0), B-j(z) (not equivalent to 0) (j = 0,1, ... ,k - 1) are meromorphic functions. Under some conditions, we determine the hyper-order of these solutions.

• 出版日期2013-3