Abstract
This paper provides a new proof of the existence and uniqueness of the solution for a nonlinear boundary value problem
{(1+delta y)y']' + 2x(1+gamma y)y' = 0, 0 < x < infinity, y(0) = 0, y(infinity) = 1,
which describes the study of two-phase Stefan problems on the semi-infinite line [0, infinity). This result considerably extends the analysis of a recent work. A highly accurate analytic approximate solution of this problem is also provided via the Adomian decomposition method.