Abstract
Under certain assumptions on the functions f, G and h, we establish one new criterion on the operator L defined on C(I) by
Lu(t) = integral(w)(0) G(t, s)h(s) f(u(s)) ds, t is an element of I, omega is an element of {1, infinity},
to guarantee that the operator equation has at least three solutions, where I = [0, 1] if omega = 1 and I = [0, infinity) if omega = infinity, via the Leguette-Williams fixed point theorem. Two examples are given to demonstrate our main result.