A boundary value problem from draining and coating flows involving a third-order ordinary differential equation (Q1392760)

The authors study the boundary value problem \[ y'''= f(y),\quad x>0,\quad y(0)= 0,\quad y(+\infty)= 1,\quad y'(+\infty)= 0,\quad y''(+\infty)= 0. \] \(f(y)\) is satisfying the conditions: There exists a positive number \(\lambda\) and a function \(g(y)\) such that \(f(y)= (1- y)^\lambda g(y)\). \(g(y)\) is defined, continuous and nonincreasing on \((0,1]\) and \(g(y)\geq 1\).