Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 123283, 15 pages
doi:10.1155/2009/123283
Triple Positive Solutions for Third-Order m-Point Boundary Value Problems on Time Scales
Jian Liu1
and Fuyi Xu2
1School of Statistics and Mathematics Science, Shandong Economics University, Jinan, Shandong 250014, China
2School of Science, Shandong University of Technology, Zibo, Shandong 255049, China
Abstract
We study the following third-order m-point boundary value problems on time scales (φ(uΔ∇))∇+a(t)f(u(t))=0, t∈[0,T]T, u(0)=∑i=1m−2biu(ξi), uΔ(T)=0, φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), where φ:R→R is an increasing homeomorphism and homomorphism and φ(0)=0, 0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.