Copyright © 2009 Hua Su. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the existence of positive solutions for the following nonlinear m-point boundary value problem for an increasing homeomorphism and homomorphism with sign changing nonlinearity: {(ϕ(u′(t)))′+a(t)f(t,u(t))=0, 0<t<1, u′(0)=∑i=1m−2aiu′(ξi), u(1)=∑i=1kbiu(ξi)−∑i=k+1sbiu(ξi)−∑i=s+1m−2biu′(ξi), 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 is given. The conclusions in this paper essentially extend and improve the known results.