Uniqueness for a class of nonlinear initial value problems (original) (raw)

This article addresses the uniqueness of nonnegative solutions for a specific class of nonlinear initial value problems characterized by the equation x' = p(t)x^a + q(t) with the initial condition x(0) = 0, where p and q are integrable functions. A theorem is formulated that provides conditions for the uniqueness of solutions, building on previous work but extending it to cases where the function q can change sign. The paper not only presents a proof of the theorem, supporting it with constructive examples and counterexamples, but also clarifies the importance of the conditions imposed on the functions involved. The findings have implications for the study of semi-linear elliptic boundary value problems.