时间测度链上三点边值问题两个正解的存在性

The Existence of Two Positive Solutions to Three-Point Boundary Value Problem on Time Scales

运用锥上的Avery-Henderson不动点定理,研究了时间测度链上一类非线性三点边值问题{u^(Δ▽)(t)+h(t)f(t,u(t))=0(t∈[a,c]T),u~Δ(a)=0,αu(c)+βu~Δ(c)-u~Δ(b)=0至少2个正解的存在性,其中,T表示时间测度链,0≤a<b<c,α>0,β>1.并给出了与之相对应的线性三点边值问题解的一些性质,举例证明了所得结论的正确性.

Existence of at least two positive solutions to a nonlinear three-point boundary value problem{uΔ▽（t）＋h（t）f（t,u（t））=0 （t[a,c]？T）,uΔ（a）=0,αu（c）＋βuΔ（c）-uΔ（b）=0on time scales is considered, and the main tool is well-known Avery-Henderson fixed-point theorem in cones.The solution and some of its properties of the linear three-point boundary value problem related to the nonlinear boundary value problem are provided.At last, an example is given to demonstrate the result of this study.