Positive solutions of singular nonlinear boundary value problems

摘要

For a class of problems of the form y" = g(t,y)f(y'), 0 < t < 1, y'(0) = m ≤ 0, y(1) = 0, we prove existence of a unique positive solution with y"(t) < 0, give necessary and sufficient conditions for y'(1) > -∞, and find asymptotic formulae for y(t) and y'(t) as t → 1~-. We particularly include cases where the nonlinearity causes singularities at the endpoints of (0,1).