一类弹性梁方程多个正解的存在性

摘要

文章运用不动点指数理论和上下解方法，研究了一类四阶两点边值问题u（4）（t）＝ f （t ，u（t）），0＜ t＜1， u（0）＝ u（1）＝0， u′（0）＝ u′（1）＝0．得到了其多个正解的存在性定理，并且指出了正解和对应线性问题第一特征值之间的关系．%This paper studies a kind of fourth‐order two‐point boundary value problems u(4) (t)= f (t ,u(t)) , 0< t<1, u(0)= u(1)=0 , u′(0)= u′(1)=0 . with upper and lower solution as well as fixed‐point index theorem .It obtains the result about the existence of its multiple positive solution ,and indicates the relations between the positive solutions and the first eigenvalue of the relevant linear problem .