Open Access Research Article

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

Chenghua Gao1* and Hua Luo2

Author Affiliations

1 Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

2 School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China

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Boundary Value Problems 2011, 2011:198598 doi:10.1155/2011/198598

Published: 27 June 2011

Abstract

We discuss the existence of solutions for the first-order multipoint BVPs on time scale : , , , where is a parameter, is a fixed number, , is continuous, is regressive and rd-continuous, , , , , and . For suitable , some existence, multiplicity, and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index.