This article is concerned with solving nonlinear inverse problems to recover the second-order nonlinear Sturm–Liouville operators, probably including a nonlinear convective term, which refers to over-specified boundary data. Utilising a homogenization approach with the boundary data, a series of boundary functions are obtained and consist of a linear space combined with the zero element. The energetic functional both qualifying the homogeneous boundary conditions and maintaining the energy is presented in the linear space based on the energetic boundary functions. The multiplier can be decided by solving a nonlinear equation. The linear systems utilized in rebuilding the uncertain leading coefficient function as well as the potential function in the nonlinear Sturm–Liouville operator are improved, so that the iterative algorithms converge rapidly. Numerical examples provided indicate that the presented method is well capable of recovering the nonlinear Sturm–Liouville operators with a nonlinear convective term.

中文翻译：

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使用边界函数方法求解非线性对流项的非线性逆 Sturm-Liouville 问题

本文涉及求解非线性逆问题以恢复二阶非线性 Sturm-Liouville 算子，其中可能包括一个非线性对流项，它指的是过度指定的边界数据。利用边界数据的均质化方法，获得一系列边界函数，并由与零元素组合的线性空间组成。既限定齐次边界条件又保持能量的能量函数基于能量边界函数呈现在线性空间中。乘数可以通过求解非线性方程来确定。改进了用于重建不确定前导系数函数的线性系统以及非线性Sturm-Liouville算子中的势函数，使得迭代算法快速收敛。