摘要
The author demonstrate that the two-point boundary value problemhas a solution (A,P(8)), where III is the smallest parameter, under the minimal stringent resstrictions oil f(8), by applying the shooting and regularisation methods. In a classic paper)Kolmogorov et. al. studied in 1937 a problem which can be converted into a special case of theabove problem.The author also use the solutioll (A, p(8)) to construct a weak travelling wave front solutionu(x, t) = y((), (= x -- Ct, C = AN/(N + 1), of the generalized diffusion equation with reactionO { 1 O.IN￣1 OUI onde L k(u) i ox: &) ￣ & = g(u),where N > 0, k(8) > 0 a.e. on [0, 1], and f(s):= ac i: g(t)kl/N(t)dt is absolutely continuouson [0, 11, while y(() is increasing and absolutely continuous on (--co, +co) and(k(y(())ly,(OI'), = g(y(()) -- Cy'(f) a.e. on (--co, +co),y(￣oo) ￣ 0, y(+oo) ￣ 1.
