Asymptotic formulae of Liouville--Green type for higher even-order equations (Q1776802)

The asymptotic formulae of Liouville-Green type of the fundamental solutions of the \(2m\)th-order differential equation \[ (p_0y^{(m)})^{(m)}+\sum\limits_{j=0}^{m-1}\Big[\dfrac12\big\{(q_{m-j}y^{(j)})^{(j+1)}+ (q_{m-j}y^{(j+1)})^{(j)}\big\}+(p_{m-j}y^{(j)})^{(j)}\Big]=0 \eqno(1) \] are investigated. A theorem on the asymptotic behaviour at infinity of the fundamental solutions of (1) is proved. The author shows that some results known earlier are contained in this theorem as particular cases.