Notes on Admissible Solutions of a Class of Dierential Equations
Weiran Lü *
Department of Mathematics, China University of Petroleum, Qingdao, 266580, People's Republic of China.
Nana Liu
Department of Mathematics, China University of Petroleum, Qingdao, 266580, People's Republic of China.
Qiuying Li
Department of Mathematics, China University of Petroleum, Qingdao, 266580, People's Republic of China.
Chungchun Yang
Department of Mathematics, Nanjing University, Nanjing 210093, People's Republic of China.
*Author to whom correspondence should be addressed.
Abstract
Aims/ objectives: Let Q1; Q2 and Q3 be three non-vanishing meromorphic functions, and be an entire function. In this paper, we consider the dierential equation of the form: 
and derive some necessary conditions ( in terms of Qj (j = 1; 2; 3) and ) for the existence of an admissible meromorphic solution f of the above equation. As a consequence of the studies, particularly we are able to conrm partially the validity of Brück Conjecture raised in studying value sharing of an entire function and its rst derivative.
Keywords: Nevanlinna theory, admissible solutions, dierential equation, haring value, brück conjecture.