测度链上一阶非线性边值问题的多解性

Multiple Positive Solutions to Nonlinear First-Order Boundary Value Problems on Time Scales

讨论如下测度链上一阶非线性边值问题xΔ(t)=f(x(σ(t))),t∈[0,T]Tx(0)=ηx(σ(T{))通过运用Krasnosel’skii’s不动点定理并联合Leggett-Williams不动点定理获得该问题4个正解的存在性准则.

In this paper,existence criteria of four positive solutions to the following nonlinear first-order boundary value problem on time scales xΔ（t）=f（x（σ（t）））,t∈Tx（0）=ηx（σ（T））are established by using the fixed-point theorem which combines Krasnosel＇skii＇s fixed-point theorem with the Leggett-Williams fixed-point theorem.An example is given to illustrate the significance of the main results obtained.