二阶四点边值问题的三解存在性

Existence of three solutions for some second-order four-point boundary value problems

讨论了二阶四点边值问题:-x″(t)=f(t,x(t),x′(t)),t∈I=[0,1];x(0)=ax(ξ),x(1)=bx(η),其中0<ξ<η<1,0≤a,b≤1,f:[0,1]×[0,∞]→[0,∞]是连续的。利用拓扑度理论讨论了其多个解的存在性。

The second-order four-point boundary value problem -x （t）=f（t,x（t）,x＇（t））,t∈I=[0,1];x（0）=ax（ξ）,x（1）=bx（η） was studied, where 0〈ξ〈η〈1,0≤a,b≤1,f：[0,1]×[0,∞]→[0,∞]are non-negative continuous functions. Some degree theory arguments were used to get the multiplicity result.