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Positive Solutions of Second Order Discrete Problem on Infinite Intervals
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In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals{-△2u(x-1)=f(x,u(x),△u(x-1)),x ∈ N,u(0)-a△u(0)=B,△u(∞)=C,where △u(x)=u(x+1)-u(x)is the forward difference operator,N={1,2,...,∞},f:(N)×(R)+×(R)+→(R)+is continuous,a＞0,B and C are nonnegative constants,(R)+=[0,+∞),△u(∞)=limx→∞ △u(x).
positive solutionssecond order discrete problemsinfinite intervalsfixed-point theorem in cones
Haiyi WU、Tianlan CHEN
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Department of Mathematics,Northwest Normal University,Gansu 730070,P.R.China
National Natural Science Foundation of ChinaDepartment of Education University Innovation Fund of Gansu Province
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