Existence results for time scale boundary value problem

Abstract

In this paper, we establish some existence results for positive solutions to a class of singular boundary value problem on time scale by using the Krasnosel'skii fixed point theorem. Two examples are presented as applications. The conditions we used in this paper are different from those in [D.R. Anderson, Eigenvalue intervals for a two-point boundary value problem on a measure chain, J. Comput. Appl. Math. 141 (2002) 57–64; C.J. Chyan, J. Henderson, Eigenvalues problems for nonlinear differential equations on a measure chain, J. Math. Anal. Appl. 245 (2000) 547–559; L.H. Erbe, A. Peterson Positive solutions for nonlinear differential equation on a measure chain, Math. Comput. Modelling 32 (2000) 571–585; L.H. Erbe, H.Y. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994) 743–748; J. Henderson, H.Y. Wang, Positive solutions for nonlinear eigenvalue problems, J. Math. Anal. Appl. 208 (1997) 252–259; C.H. Hong, C.C. Yeh, Positive solutions for eigenvalue problems on a measure chain, Nonlinear Anal. 51 (2002) 499–507; W.C. Lian; W.F. Wong; C.C. Yeh, On the existence of positive solutions of nonlinear differential equations, Proc. Amer. Math. Soc. 124 (1996) 1117–1126; J. Liang, T.J. Xiao, Z.C. Hao, Positive solutions of singular differential equations on measure chain, Comput. Math. Appl. 49 (2005) 651–663].