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Position: Home > Articles > Positive Solutions to m-point Boundary Value Problems for Second Order Dynamic Equations on Time Scales Journal of Hebei Normal University of Science & Technology 2015,29 (2) 20-26

时标上二阶动力方程m点边值问题的正解

作  者:
武利猛;张娟;申玉发;郑国萍;杨晓静
单  位:
河北科技师范学院数学与信息科技学院;河北科技师范学院科研处
关键词:
时标;边值问题;正解
摘  要:
研究了时标上二阶动力方程m点边值问题uΔΔ(t)+q(t)f(t,u(t))=0,t∈[t1,t2],uΔ(t1)=∑m-2i=1biuΔ(ξi),au(t2)+βuΔ(t2)=∑m-2i=1aiu(ξi)。借助于Guo-Krasnosel'skii不动点定理和Leggett-Williams不动点定理得到了此问题至少存在2个正解和3个正解的判别条件,并通过举例阐述了主要结果。
译  名:
Positive Solutions to m-point Boundary Value Problems for Second Order Dynamic Equations on Time Scales
作  者:
WU Li-meng;ZHANG Juan;SHEN Yu-fa;ZHENG Guo-ping;YANG Xiao-jing;School of Mathematics and Information Technology,Hebei Normal University of Science & Technology;Office of Science and research,Hebei Normal University of Science & Technology;
关键词:
time scales;;boundary value problem;;positive solutions
摘  要:
This paper is concerned with m-point boundary value problems for second order dynamic equations on time scales uΔΔ( t) + q( t) f( t,u( t)) =0,t∈[t1,t2],uΔ( t1) = ∑m- 2i = 1biuΔ( ξi),αu( t2) + βuΔ( t2) = ∑m- 2i = 1aiu( ξi).By means of Guo-Krasnosel'skii and Leggett-Williams fixed point theorems in cones,some new results are obtained for the existence of at least two and three positive solutions of the above problems. Meanwhile,two examples are given to illustrate the main result.

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