Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 143040, 16 pages
doi:10.1155/2008/143040

Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales

Abstract

We study the following third-order p-Laplacian m-point boundary value problems on time scales: (ϕp(uΔ∇))∇+a(t)f(t,u(t))=0, t∈[0,T]T, βu(0)−γuΔ(0)=0, u(T)=∑i=1m−2aiu(ξi), ϕp(uΔ∇(0))=∑i=1m−2biϕp(uΔ∇(ξi)), where ϕp(s) is p-Laplacian operator, that is, ϕp(s)=|s|p−2s, p>1,  ϕp−1=ϕq, 1/p+1/q=1,  0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.