Existence results for time scale boundary value problem

  • Authors:

  • Zhao-Cai Hao;Jin Liang;Ti-Jun Xiao

  • Affiliations:

  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People's Republic of China and Department of Mathematics, Qufu Normal University, Qufu, Shandong, People's R ...;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People's Republic of China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, People's Republic of China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2006

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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].