Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 976406, 14 pages
doi:10.1155/2009/976406

Solutions for m-Point BVP with Sign Changing Nonlinearity

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.