MONOTONE ITERATIVE METHOD AND REGULAR SINGULAR NONLINEAR BVP IN THE PRESENCE OF REVERSE ORDERED UPPER AND LOWER SOLUTIONS

Monotone iterative technique is employed for studying the existence of solutions to the second-order nonlinear singular boundary value problem -(p(x)y'(x))' + p(x) f (x, y(x), p(x) y' (x)) = 0 for 0 < x < 1 and y'(0) = y'(1) = 0. Here p(0) = 0 and xp'(x)/p(x) is analytic at x = 0. The source function f(x, y, py') is Lipschitz in py' and one sided Lipschitz in y. The initial approximations are upper solution u(0)(x) and lower solution v(0)(x) which can be ordered in one way v(0)(x) <= u(0)(x) or the other u(0)(x) <= v(0)(x).