摘要
In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：x″（t）＋f（t,x（t））=0,0〈t〈1,x′（0）=0,x（1）＋δx′（η）=0,where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.
In this paper, the existence of monotone positive solution for the following secondorder three-point boundary value problem is studied：x″（t）＋f（t,x（t））=0,0〈t〈1,x′（0）=0,x（1）＋δx′（η）=0,where η ∈ （0, 1）, δ∈ [0, ∞）, f ∈ C（[0, 1] × [0, ∞）, [0, ∞））. Under certain growth conditions on the nonlinear term f and by using a fixed point theorem of cone expansion and compression of functional type due to Avery, Anderson and Krueger, sufficient conditions for the existence of monotone positive solution are obtained and the bounds of solution are given. At last, an example is given to illustrate the result of the paper.
基金
the Natural Science Foundation of Zhejiang Province of China (Y605144)
the XNF of Zhejiang University of Media and Communications (XN08001)
