On the WKB method for certain third order ordinary differential equations (Q1190671)

The authors consider the WKB type asymptotic expansions of solutions to third order linear ordinary differential equations of the form \(\varepsilon^ 3y'''+\varepsilon^ 2p_ 1(x)y''+\varepsilon p_ 2(x)y'+p_ 3(x)y=0\), in the whole complex \(x\)-plane. The formal solutions are constructed by the WKB method; an existence theorem is given; questions such as the Stokes curve configuration, existence of admissible domains, the connection rules in the whole complex \(x\)-plane are considered, which had been considered by other authors for second order ordinary differential equations.