具有变号格林函数的四阶三点边值问题正解的存在性

Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green's Function

应用迭代法研究四阶三点边值问题u^((4))(t)=f(t,u(t)),t∈[0,1],u′(0)=u″(η)=u'''(0)=u(1)=0的可解性,得到了该问题正解的存在性.其中f:[0,1]×[0,+∞)→[0,+∞)连续,η∈[3^(1/2)/3,1]为常数.在格林函数变号的情形下,仍可获得该问题正解的存在性定理,并且此解是单调递减的,使得该问题正解的存在性不再局限于格林函数是正的.

We applied iterative method to study the solutions for a fourth-order three-point boundary value problems, and obtained the existence of positive solutions of the problem u-（4）（t）=f（t,u（t））,t∈[0,1],u′（0）=u″（η）=u＇＇＇（0）=u（1）=0 where f：[0,1]×[0,＋∞）→[0,＋∞） is continuous, η∈[√3/3,1] is a constant. In the case of sign-changing Green＇s function, the existence theorem of positive solution of this problem can be obtained, and the solution is monotonically decreasing, the existence of the positive solution of this problem is no longer limited to the positive Green＇s function.