Nonexistence for the Kassoy problem. (English) Zbl 0645.34008

Bebernes, J.; Troy, W.

SIAM J. Math. Anal. 18, 1157-1162 (1987).

The authors prove that the Kassoy problem \[ y''-\frac{x}{2}y'+e^ y- 1=0,\quad y(0)=\alpha,\quad y'(0)=0,\quad \alpha \in R, \] has no solution which has the asymptotic property \(y(x)\sim -2\ell nx+k\) as \(x\to \infty\).

Reviewer: N.L.Maria

MSC:

34A34

Nonlinear ordinary differential equations and systems

Keywords:

combustion; supercritical; final time asymptotic analysis; Kassoy problem