时标上二阶动力方程m点边值问题的正解

Positive Solutions to m-point Boundary Value Problems for Second Order Dynamic Equations on Time Scales

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。

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-2∑i=1biuΔ（ξi）,au（t2）＋βuΔ（t2）=m-2∑i=1aiu（ξi） By means of Guo-KrasnoselSkii and Leggett-WiUiams fixed point theorems in cones, some new results are ob-mined for the existence of atieast two and three positive solutions of the above problems. Meanwhile, two ex- amples are given to illustrate the main result.