Abstract
Let 0 0, f″(u) > 0 for u > 0. By using Green’s function, the problem is converted into an integral equation. It is shown that there exists tb such that for 0 ≤ t 0, f″(u) > 0 for u > 0. By using Green’s function, the problem is converted into an integral equation. It is shown that there exists tb such that for 0 ≤ t < tb, the integral equation has a unique nonnegative continuous solution u; if tb is finite, then u is unbounded in [0, tb). Then, u is proved to be the solution of the original problem.
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