Admissible meromorphic solutions of algebraic differential equations (Q713454)

Let \(\sum_{\lambda\in I}a_{\lambda}y^{\lambda_0}(y')^{\lambda_1}\dotsm(y^{(n)})^{\lambda_n}=0 \) be an algebraic differential equation, where \(I\) is an index set, \(\lambda=(\lambda_0, \lambda_1, \dotsc, \lambda_n)\) and \(a_{\lambda}\) are meromorphic functions. The authors prove that the algebraic differential equation has no admissible transcendental meromorphic solutions satisfying \(N(r, f)=S(r, f)\) if the equation has only one dominant term.