一类高阶迭代边值问题的正解

Positive Solutions of a Class of Boundary Value Problem for High Order Differential-Iterative Equations

基于Krasnosel'skii不动点定理考虑了一类四阶迭代边值问题u''''(t)=f(t,u(t),u(αu(t))),0≤t≤1,u(0)=u'(0)=u''(1)=u'''(1)=0正解的存在性.通过估计解的界,获得了上述边值问题分别存在和不存在正解的几组充分条件.最后给出例子说明了主要结果的可行性.

Based on the Krasnoserskii fixed-point theorem of cone expansion-compression type, the positive solutions of a class of BVP for high order differential-iterative equations u＂＂（t）=f（t,u（t）, u（αu（t）））, 0≤t≤1,with boundary conditions u（0） = u＇（0） = u＂（1） = u＇＂（1） = 0, are investigated. Some sufficient conditions for existence and nonexistence results for the boundary value problem are established. An example is given at the end of the paper to illustrate the main results.