EXISTENCE OF THREE SOLUTIONS FOR A TWO-POINT SINGULAR BOUNDARY-VALUE PROBLEM WITH AN UNBOUNDED WEIGHT

We show the existence of three solution for the singular boundary value problem -z " = h(t) f (z) /z(beta) in (0, 1), z(t) > 0 in (0, 1), z(0) = z(1) = 0, where 0 < beta < 1, f is an element of C-1([0,infinity), (0, infinity)) and h is an element of C((0, 1], (0, infinity)) is such that h(t) <= C/t(alpha) on (0, 1] for some C > 0 and 0 < alpha < 1 - beta. When there exist two pairs of sub-supersolutions (psi 1, phi 1) and (psi 2, phi 2) where psi(1) < psi(2) <= phi(1), psi(1) < phi(2) < c1 with 02 QL 0 2, and 02,02 are strict sub and super solutions. The establish the existence of at least three solutions satisfying z(1) is an element of [psi(1),phi(2)], z(2) is an element of [psi(2),phi(1)] and z3 is an element of [psi(1),phi(2)]\([is an element of [psi(1),phi(2)]boolean OR is an element of [psi(1),phi(2)]).