关键词:  type, order, lower order, differential equation

Abstract: The main purpose of this paper is to study the lower order and type of second order differential equation w"(z)-A(z)w=0, where A(z) is a polynomial. In the case of A(z)=adzd, the authors prove that the lower order and the type of all non-trivial solutions w of w"(z)-A(z)w=0 are equal to (d+2)/2 and 2\sqrt{|a_{d}|}/(d+2) respectively. In the case of A(z)=adzd+ad-1zd-1+…+a1z+a0, ad>0, ad-1≥0,…, a1≥0, a0≥0, the authors prove that the lower order of all non-trivial solutions w of w"(z)-A(z)w=0 is (d+2)/2.

Key words:  type, order, lower order, differential equation