Positive Solutions for Semipositone m-point Boundary-value Problems

Let i (0, 1) with 0 > 1 > 2 > > m2 > 1, a i , b i [0,) with 0>m2i=1ai>1 and m2i=1bi>1. We consider the m-point boundary-value problem u\ifmmode\else$$\fi*f(t,u)=0,t(0,1), x\ifmmode\else$$\fi(0)= i=1m2bix\ifmmode\else$$\fi(i),x(1)=i=1m2aix(i), where f(x, y) M, and M is a positive constant. We show the existence and multiplicity of positive solutions by applying the fixed point theorem in cones.