Multiple positive solutions for semi-positone m-point boundary value problems

In this article, we establish the existence of at least two positive solutions for the semi-positone m-point boundary value problem with a parameter u" (t) + lambda f(t, u) = 0, t is an element of (0, 1), u'(0) = (m-2)Sigma(i=1) b(i)u'(xi(i)), u(1) = (m-2)Sigma(i=1) a(i)u(xi(i)), where lambda > 0 is a parameter, 0 < xi(1) < xi(2) < ... <xi(m-2) < 1 with 0 < (m-2)Sigma(i-1) a(i) < 1, (m-2)Sigma(i-1) b(i) < 1, a(i), b(i) is an element of [0,infinity) and f( t, u) >= - M with M is a positive constant. The method employed is the Leggett-Williams fixed-point theorem. As an application, an example is given to demonstrate the main result.