Existence of explosive solutions to two-point boundary value problems Original Research Article

By the quadrature method, we show that if there exists α ≤ 2 such that View the MathML sourcelim⁡s→+∞sup⁡f(s)s(ln⁡s)α=L∈[0,∞), Turn MathJax on then, the problem mml has no solution in C2(0,1), for any λ > 0; and if there exists a > 2 such that lims→+∞ inf(f (s)/s(ln s)α) = L E (0, ∞], then, the problem has a solution u ∈ C2(0, 1) for some λ > 0.