A quasilinearization algorithm is developed for boundary value problems at resonance. To do so, a standard monotonicity condition is assumed to obtain the uniqueness of solutions for the boundary value problem at resonance. Then the method of upper and lower solutions and the shift method are applied to obtain the existence of solutions. A quasilinearization algorithm is developed and sequences of approximate solutions are constructed, which converge monotonically and quadratically to the unique solution of the boundary value problem at resonance. Two examples are provided in which explicit upper and lower solutions are exhibited.

中文翻译：

---

共振时的拟线性化和边值问题

针对共振时的边值问题，开发了一种准线性化算法。为此，假定使用标准单调性条件来获得共振时边值问题的解的唯一性。然后采用上下解法和平移法求解的存在性。提出了一种拟线性化算法，并构造了近似解的序列，这些序列单调和二次收敛于共振时边值问题的唯一解。提供了两个示例，其中展示了显式的上下解决方案。