一类四阶两点边值问题正解的存在性

Existence of positive solutions for a fourth-order two-point boundary value problem

运用上下解方法及拓扑度理论讨论了非齐次边界条件下四阶两点边值问题u″″(t)=f(u(t)),t∈(0,1),u(0)=u″(0)=u″(1)=0,u(1)=λ,其中λ>0为参数,f∈C([0,+∞),[0,+∞)).在非线性项满足一定的增长条件下,获得了上述问题存在正解时λ的取值范围.

In this paper,by using the lower and upper solutions method and the topological degree theory,we study the following fourth-order two-point boundary value problem u″″（t） = f（u（t））,t ∈（0,1）,u（0） = u″（0） = u″（1） = 0,u（1） = λ with nonhomogeneous boundary condition,where λ 0 is a parameter,f ∈ C（[0,＋∞）,[0,＋∞））.Under certain growth conditions on f,we determine the intervals of λ in which the above problems exist positive solutions.