研究了无穷限第一类Fredholm积分方程的求解问题。第一类Fredholm方程是不适定问题，解不稳定，必须采用正则化方法处理。为此，利用Tikhonov正则化方法研究这类问题，其中，展平泛函按标准的Sobolev空间范数来构造，正则化参数则通过Morozov偏差原理来选取。最后，证明了由此获得的正则化解存在唯一性。并讨论了求解正则化解的变分方法。
Abstract
The regularization method for solving the first kind Fredholm integral equation in [0, +∞] was studied in this paper. This kind of equation is an ill-posed problem which means the solution of this problem is instable. Therefore, it is necessary to investigate this problem with regularization method. We employed Tikhonov regularization method to research this problem and used norm of Sobolev space to construct flattening function. The regularization parameter was chosen by Morozov principle. In the end, we proved the existence and uniqueness of the regularization solution. Furthermore, we discussed the variationa method for solving regularization solutions.
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