Consider the class of four point nonlinear BVPs [Formula: see text] [Formula: see text] where [Formula: see text] is continuous, [Formula: see text], [Formula: see text] such that [Formula: see text] and [Formula: see text]. In this paper, we demonstrate an iterative technique. The iterative scheme is deduced by using quasilinearization. Then we consider upper-lower solutions in well ordered and reverse ordered cases and prove existence of solutions under some sufficient conditions. We show that under certain conditions, generated sequences are monotone, uniformly convergent and converges to the solution of the above problem. We also provide examples which validate that all the conditions derived in this paper, are realistic and can be satisfied. We have also plotted upper and lower solutions for the test examples and have shown that under the conditions, the derived upper and lower solutions are monotonic in nature.

中文翻译：

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一类具有逆序上下解的四点BVP的单调迭代技术

考虑四点非线性 BVP 类 [公式：见正文] [公式：见正文] 其中 [公式：见正文] 是连续的，[公式：见正文]，[公式：见正文] 使得 [公式：见正文] 和 [公式：见正文]。在本文中，我们展示了一种迭代技术。通过使用拟线性化推导出迭代方案。然后我们考虑在良序和逆序情况下的上下解，并在一些充分条件下证明解的存在性。我们表明，在一定条件下，生成的序列是单调的、一致收敛的并且收敛到上述问题的解。我们还提供了一些例子来验证本文得出的所有条件都是现实的并且可以满足。