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Bifurcation structure of asymptotically linear second-order #br# semipositone discrete boundary value problem#br#

ZHANG Lu, MA Ru-yun   

  1. College of Mathematics and Statistics, Northwest Normal University,
    Lanzhou 730070, Gansu, China
  • Received:2013-10-14 Online:2014-03-20 Published:2014-05-29

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Abstract: It is studied that  the existence of positive solutions of second-order semipositone discrete boundary value problem with the nonlinearity satisfies asymptotically linear conditions,
-Δ2u(t-1)=λf(t,u(t)), t∈［1,T］Z,
αu(0)-βΔu(0)=0, γu(T)+δΔu(T)=0,
where λ is a positive parameter, f:［1,T］Z×R+→R is continuous, The proofs of the main results are based on the topological degree techniques and bifurcation theory.

Key words: positive solutions, Sturm-Liouville boundary value conditions, bifurcation theory, semipositone problem, topological degree

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