Unbounded solutions of second order discrete BVPs on infinite intervals

Volume 9, Issue 2, pp 357--369 http://dx.doi.org/10.22436/jnsa.009.02.02

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Authors

Hairong Lian - School of Science, China University of Geosciences, Beijing 100083, P. R. China. Jingwu Li - School of Science, China University of Geosciences, Beijing 100083, P. R. China. Ravi P Agarwal - Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas 78363, USA.

Abstract

In this paper, we study Sturm-Liouville boundary value problems for second order difference equations on a half line. By using the discrete upper and lower solutions, the Schäuder fixed point theorem, and the degree theory, the existence of one and three solutions are investigated. An interesting feature of our existence theory is that the solutions may be unbounded.

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Keywords

• Coincidence point
• discrete boundary value problem
• infinite interval
• upper solution
• lower solution
• degree theory common fixed point.

MSC

•  47H10
•  54H25
•  54C60

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