The existence of countably many positive solutions for nonlinear singular m-point boundary value problems on time scales

In this paper, by introducing a new operator, improving and generating a p-Laplace operator for some p>1, we study the existence of countably many positive solutions for nonlinear boundary value problems on time scales vertical bar phi(u(Delta))vertical bar(del) + a(t) f(u(t))=0, t is an element of vertical bar 0.T vertical bar(T). u(0) = Sigma(m-2)(i=1) alpha(i)u(xi(i)). u(Delta)(T)=0 where phi: R -> R is the increasing homeomorphism and positive homomorphism and phi(0)=0. We show the sufficient conditions for the existence of countably many positive solutions by using the fixed-point index theory and a new fixed-point theorem cones. (C) 2008 Elsevier B.V. All rights reserved.