[For parts I-III see SIAM J. Appl. Math. 42, 502-531 (1982; Zbl 0515.34058
), ibid. 45, 687-707 (1985; Zbl 0623.34050
), ibid. 45, 708-734 (1985; Zbl 0623.34051
The authors study the model $\epsilon y''(x,\epsilon)+[y(x- 1,\epsilon)y(x,\epsilon)]'=f(x)$, $0<x<1$; $0<\epsilon \ll 1$; $y(x,\epsilon)=\phi (x)$ on -1$\le x\le 0$, and $y(1,\epsilon)=\gamma$. Integrating both sides of the equation and using singular perturbation techniques an exact solution for the constant case is constructed. Also in this case some discussion regarding the existence and uniqueness of the solution is presented. By a combination of singular perturbation analysis and numerical computations the authors give a comprehensive treatment of the full spectrum of solution behavior of the model with $\phi\ne 0$ on [-1,0].