On a generalization of the Chazy equation with a movable singular line

摘要

We generalize a third-order Chazy equation with a movable singular line, which has only negative resonances. For differential equations of order 2n+1 with resonances -1,-2, ..., -(2n + 1), we study the convergence of the series representing their solutions, the existence of rational solutions, the invariance of these equations under certain transformations, and the existence of three-parameter solutions with a movable singular line. [PUBLICATION ABSTRACT]