Boundary Value Problems
Volume 2011 (2011), Article ID 198598, 15 pages
Research Article

Positive Solutions to Nonlinear First-Order Nonlocal BVPs with Parameter on Time Scales

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China

Received 4 May 2010; Accepted 3 June 2010

Academic Editor: Daniel Franco

Copyright © 2011 Chenghua Gao and Hua Luo. 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.


We discuss the existence of solutions for the first-order multipoint BVPs on time scale 𝕋: uΔ(t)+p(t)u(σ(t))=λf(t,u(σ(t))), t[0,T]𝕋, u(0)-i=1mαiu(ξi)=0, where λ>0 is a parameter, T>0 is a fixed number, 0,T𝕋, f:[0,T]𝕋×[0,)[0,) is continuous, p is regressive and rd-continuous, αi0, ξi𝕋, i=1,2,,m, 0=ξ0<ξ1<ξ2<<ξm-1<ξm=σ(T), and 1-i=1m(αi/ep(ξi,0))>0. For suitable λ>0, some existence, multiplicity, and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index.