Regions of existence and uniqueness for singular two-point boundary value problems

A monotone iterative technique with lower and upper solutions is presented to identify the regions of existence for the solutions of singular two-point boundary value problems \begin{align*} &y''(x)+ \frac{p'(x)}{p(x)}y'(x)= f(x,y(x)), \quad x \in [0,b], \\ &y'(0) = 0, \quad Ay(b)+By'(b) = C, \quad A>0, B \ge 0, C \ge 0, \end{align*} without requiring the monotonicity conditions on $f(x,y)$. Under an additional condition on $f(x,y)$, uniqueness of the solution is also established. These existence and uniqueness results are constructive and complement the existing results. Four examples including some engineering problems are given to illustrate the applicability of the proposed approach.