On a second-order boundary value problem arising in combustion theory
We obtain existence and uniqueness results for the boundary-value problem y" = x2 — y2, y(x) ~ +x as x —> + oo. Our main result shows that there are precisely two solutionsy+(x) > — |x| andy_(x) < — | x |. Only the latter is of physical interest in the problem in combustion theory from which the equation arises.