论文标题
在半无限间隔中定义的BVP的存在和唯一性：迭代转换方法的见解
Existence and Uniqueness of BVPs Defined on Semi-Infinite Intervals: Insight from the Iterative Transformation Method
论文作者
论文摘要
这项工作涉及在半无限间隔中定义的边界价值问题的存在和唯一性。这类问题很少承认已知的解决方案，因此，在尝试通过分析或数值手段得出近似解决方案之前，有关其适当性的理论信息至关重要。在这种情况下，我们的最大贡献是数值测试的定义，用于研究在半无限间隔内定义的边界问题解决方案的存在和唯一性。主要结果是由定理将存在和唯一性问题与迭代转换方法公式中隐含定义的函数的真实零的数量相关的定理给出。结果，我们可以通过研究该功能的行为来研究解决方案的存在和独特性。在这种情况下，数值测试通过两个示例说明了我们发现有意义的数值结果。
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their well-posedness is essential before attempting to derive an approximate solution by analytical or numerical means. Our utmost contribution in this context is the definition of a numerical test for investigating the existence and uniqueness of solutions of boundary problems defined on semi-infinite intervals. The main result is given by a theorem relating the existence and uniqueness question to the number of real zeros of a function implicitly defined within the formulation of the iterative transformation method. As a consequence, we can investigate the existence and uniqueness of solutions by studying the behaviour of that function. Within such a context the numerical test is illustrated by two examples where we find meaningful numerical results.
