Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (3): 337-343.

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Positive Solutions for First-order PBVPs on Time Scales

  

  1. School of Applied Mathematics, Guangdong University of Technology

  • Received:2010-09-09 Online:2012-09-30 Published:2023-03-21
  • About author:SONG Chang-xiu(1975-), male, native of Laiyang, Shandong, an associate professor of Guangdong University of Technology, Ph.D., engages in functional differential equations.
  • Supported by:
    Supported by the NNSF of China(10871052, 109010600); Supported by the NSF of Guangdong  Province(10151009001000032)

Abstract: In this paper, the author studies the following nonlinear dynamic equation {x△(t) = r(t)x(σ(t)) + f(t, x(σ(t))), t ∈ [0, T ], x(0) = x(σ(T )). By applying and improving the generalized form of Leggett-Williams fixed point theorem, sufficient conditions are established for the existence of positive solutions.

Key words: time scale, positive solutions, fixed point

CLC Number: