On the uniqueness of continuous positive solution for a non-linear integral equation whose singularity lies in the reciprocal of the solution

In this article, we consider the following non-linear singular integral equation y(t) = f(t) + integral(1)(0) k(t,s)1/[y(s)(alpha)]dsin the space of continuous functions on a bounded and closed interval [0,1] for f is an element of C[0,1] with f>0, the kernelk (t,s) is a non-negative continuous function on[0,1]x[0,1] and alpha>0 fixed parameter. The non-linearity in the considered equation is singular at the dependent variable y=0. The existence of a continuous positive solution of this integral equation is well established in the literature. We determine the range of alpha that guarantees the uniqueness of the continuous positive solution of the integral equation