On Solutions of Ordinary Differential Equations Arising from a Model of Crystal Growth

The properties of the solutions of the equations φ′″ + φ′ = ?e^φ and φ′″ + φ′ = 1/(2φ) in the complex plane are discussed. Both equations have Stokes phenomena as the imaginary axis is crossed. The Stokes multiplier of the subdominant term in each case is accurately calculated by transforming the equation into an integral equation by using a Laplace integral. The existence and uniqueness of the solutions of these integral equations are also discussed.