Differential Equation with No Meromorphic Solution
XIONG Cheng ji(Department of Mathematics, Huaiyin Teachers College, Huaian 223001, China)
Consider the differential equation q(f)P+c=0 , where q(f)=f n+b n-1 f n-1 +...+b 1f+b 0, n≥1, b 0, b 1, ..., b n-1 are small functions of f , P is a differential multinomial with small function coefficients and c(z)0 is a small function of f . Xinhou Hua obtained that if q(f)=f n+b(z)f m or q(f)=(f-a 1) n 1 ...(f-a k) n k , then this equation does not Possess meromorPhic solution f . In this PaPer, we Proved same result for general q(f) .