A Condition for Finite Blow-up Time for a Volterra Integral Equation

The paper is devoted to the study of the equation u(x) = ∫x0 (x − s)α − 1g(u(s))ds (α > 0, x > 0),where g is continuous and nondecreasing. Some estimates of u′ and the interval of the existence of a nontrivial solution u are given.