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中文摘要：
本文利用锥上的不动点理论和单调迭代的方法研究了一类三阶两点边值问题单调迭代正解的存在性,得到了正解存在的充分条件,同时也给出了解的相应迭代序列来逼近解,并且给出了应用实例。值得一提的是,本文所讨论的边值问题中,非线性项显含未知函数的一阶和二阶导数。
英文摘要：
In this paper, we study the existence of monotonic iteration positive solutions for a kind of three-order two-point boundary value problems, the method mainly depends on the fixed point theory in cones and the iteration technique. We give the sufficient conditions for the existence of positive solutions to the boundary value problem and establish schemes for approximating the solution. An example is also given to illustrate the effectiveness of our results. It is worthwhile to mention that the nonlinear term in the equation we studied involves the first-and second-order derivatives explicitly.
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