On Dirichlet two-point boundary value problems for the Ermakov–Painlevé IV equation - Amster, Pablo Gustavo (2015)
Two-point boundary value problems of Dirichlet-type are investigated for a hybrid Ermakov-Painlev´e IV equation. Existence and uniqueness results are established in terms of the Painlev´e parameters. In addition, it is shown how Ermakov invariants may be used to systematically obtain solutions of a coupled Ermakov-Painlev´e IV system in terms of seed solutions of the canonical integrable Painlev´e IV equation.