测度链上二阶边值问题多个正解的存在性

Existence of Multiple Positive Solutions for A Second-order Boundary Value Problem on A Measure Chain

讨论测度链上二阶边值问题,xΔΔ+k(t)f(t,x(σ(t)))=0,t∈[t1,t2],αx(t1)-βxΔ(t1)=0,γx(σ(t2))+δxΔ(σ(t2))=0正解的存在性,[t1,t2]T,T是测度链,利用Leggett-Williams不动点定理,可得该问题至少存在3个正解.

Concerned with the existence of positive solutions for a second-order boundary value problem on a measure chainx△△＋k（t）f（t,x（σ（t）））=0,t∈[t1,t2],αx（t1）-βx（t1）=0,γx（σ（t2））＋δx△（σ（t2））=0, where [ t1, t2] T, T is a measure chain. Using Leggett-Williams fixed point theorem, we show that it has at least three positive solutions.