Positive solutions for mpoint boundary value problem

In this paper, we study the existence of positive solutions for the following nonlinear mpoint boundary value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity: (Φ(u )) +a(t) f(t,u(t))=0, 0 t 1, u (0)=∑^m-2_i=1 aiu (Ɛi)- ∑ ^k_i=1 biu(Ɛi) ∑^s_i=k+1 bi u(Ɛi)\ ∑^m-2_i=s+1 b_iu (Ɛi), where Φ: R → R) is an increasing homeomorphism and homomorphism and Φ(0) = 0). The nonlinear term f may change sign. As an application, an example to demonstrate our results has given. The conclusions in this paper essentially extend and improve the known results.