Nonlinear complex differential equations with solutions in some function spaces. Issue 2 (1st February 2019) - Sun, Yu; Long, Jianren; Hu, Guangming
ABSTRACT: Sufficient conditions for their derivatives and analytic solutions of( f ( k ) ) n k + A k - 1 ( z ) ( f ( k - 1 ) ) n k - 1 + ⋯ + A 1 ( z ) ( f ′ ) n 1 + A 0 ( z ) f = A k ( z ) to be inH Φ ∞ orB α are found in this paper. On the one hand, for the case of unit disc, some generalization of earlier results given by Huusko–Korhonen–Reijonen is obtained. On the other hand, by replacing the unit disc with the simple connected domain, some sufficient conditions for their derivatives and analytic solutions of the nonlinear equations to be inH Φ ∞ orB α are also obtained.