On some generalized Painleve and Hayman type equations with meromorphic solutions in a bounded domain

The value distribution and, in particular, the numbers of a-points, have not been studied for meromorphic functions which are solutions of some complex differential equations in a given domain. Instead, the numbers of good a-points and Ahlfors islands, which play to a certain extend a role similar to that of the numbers of a-points, have been considered in some recent papers. In this paper, we consider meromorphic functions in a given domain, which are the solutions of some higher order equations and largely generalize the solutions of Painleve equations 3-6. We give the upper bounds for the numbers of good a-points and Ahlfors islands of similar solutions.