Positive solutions of m-point boundary value problems for second order differential equations with an advanced argument

In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions to m-point boundary value problem for the second order differential equation with an advanced argument {u"(t)+a(t)f(u(h(t)))=0, t isin (0,1), u(0)=0, Sigma_i=1 ^m-2 k_iu(xi_i)=u(1), where 0=xi₀<xi₁<hellip<xi_m-2<xi_m-1=1.